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THE  ESSENTIALS  OF 
LOGIC 


BY 


R.  W.  SELLARS,  Ph.D. 

Assistant  Professor  of  Philosophy 
University  of  Michigan 


BOSTON  NEW  TOBK  CHICAGO 

HOUGHTON  MIFFLIN  COMPANY 


COPYKIGHT,    I917,    BY   R.  W     SELLARS 
ALL   RIGHTS  RKSERVKD 


CAMBRIDGB  .  MASSACHUSETTS 
U   .   S   .   A 


CONTENTS 


I.  Introductory 1 

A  Definition  of  Logic  —  The  Value  of  Logic  —  The  Kinds 
of  Logic  —  Introductory  Logic  —  Relation  of  Logic  to 
Other  Sciences  —  The  Material  of  Logic  —  References. 

n.  The  Nature  and  Setting  of  Thought    .      .      .10 

What  is  Thought?  —  Discovery  and  Proof  —  The  Psy- 
chologist's View  of  Reasoning  —  Examples  of  Reasoning 

—  The  Conditions  and  Occasions  of  Thought  —  The  Set- 
ting of  Thought  —  Why  we  think  —  Processes  Preliminary 
to  Reflective  Thought  —  Fact  and  Theory  —  Knowledge  a 
Growth  —  References. 

in.  About  Terms 27 

The  Unit  of  Thought  —  The  Elements  of  the  Proposition 

—  Words  and  Terms  —  Kinds  of  Terms  —  Other  Kinds  of 
Terms  —  Connotation  and  Denotation  —  SjTionyms  for 
Connotation  and  Denotation  —  The  Inverse  Variation  of 
Connotation  and  Denotation  —  Terms  and  Meaning  — 
References. 

rV.   The  Use  and  Misuse  of  Language       ...    40 

The  Necessity  for  Language  —  Language  and  Analysis 

—  The  Logical  Law  of  Language  —  Causes  of  Ambiguity 

—  Univocal  Words  —  Equivocal  Words  —  Words  change 
their  Meanings  — Vagueness  —  Abstract  Terms  particiJarly 
subject  to  Vagueness  —  Logic  and  Language  —  References. 

V.  Classification  and  Division 50 

Classification  and  Classes  —  The  Need  for  Classification 

—  Types  of  Classification  —  Artificial  Classification  —  Nat- 
ural Classifications  —  Natural  Classification  in  the  Light 
of  Evolution  —  Character  of  Systematic  Qassification  — 
Classification  and  Division  —  Technical  Terms  used  in 
Division  —  Rules  of  Division  —  Forms  of  Division  —  Di- 
chotomous  Division  —  Classificatory  Division  —  Dangers 
to  be  guarded  against  —  References. 


n  CONTENTS 

VI.  Principlbs  of  Definition 62 

Why  Definition  is  needed  —  The  Purpose  and  Nature  of 
Definition  —  Logic  stresses  General  Terms  —  Definition 
and  Classification  —  The  Verification  of  Meaning  —  Rules 
of  Definition  —  Other  Forms  of  Definition  —  The  Pred- 
icables  —  The  Importance  of  Definition  —  References. 

Vn.  Assertions  and  Propositions 76 

An  Important  Distinction  —  Critical  vs.  Uncritical  As- 
sertion —  What  is  an  Assertion  ?  —  Levels  of  Judgment  — 
Concepts  and  Judgment  —  Judgment  defined  —  All  Knowl- 
edge Judgmental  —  The  Part  played  by  Language  —  The 
Logical  Treatment  of  Propositions  —  References. 

Vm.  The  Logic  of  Propositions 89 

A  General  Division  of  Propositions  —  The  Quality  and 
Quantity  of  Propositions  —  Symbolic  Classification  of  Prop- 
ositions —  Reduction  of  Propositions  to  Logical  Form  —  The 
Distribution  of  Terms  —  The  Graphical  Method — The  Pur- 
pose of  Logical  Analysis  —  References. 

IX.  The  Implications  of  Propositions    .      .      .      .98 

Immediate  Inference  —  The  Oppositions  of  the  Four 
Kinds  of  Propositions  —  Conversion  —  Obversion  —  False 
Obversion  —  Contraposition  —  Significance  of  Immediate 
Inference  —  References. 

X.  The  Syllogism  as  a  Mechanism         ....  107 

The  Nature  of  the  Syllogism  —  An  Analysis  of  the  Syllo- 
gism —  The  Elements  of  the  Syllogism  —  The  Rules  of  the 
Syllogism  —  The  Formal  Syllogism  and  Actual  Reasoning 
—  References. 

XI.  The  Figures  and  Moods  of  the  Syllogism       .  118 

The  Figures  of  the  Syllogism  —  The  Moods  of  the  Syllo- 
gism —  Reduction  to  the  First  Figure  —  Comparative 
Value  of  the  Figures  —  References. 

Xn.  Abbreviated     and     Expanded     Arguments  — 

Extra-Syllogistic  Arguments     ....  126 

Enthymeme  —  Prosyllogisms  and  Episyllogisms  —  Sori- 
tes —  Extra-Syllogistic  Arguments  —  References. 


CONTENTS  V 

Xni.  Hypothetical  and  Disjunctive  Syllogisms     .  132 

The  Hypothetical  Syllogism  —  The  Rule  of  the  Hypothet- 
ical Syllogism  —  The  Fallacies  of  the  Hypothetical  Syllo- 
gism —  Reduction  to  Categorical  Form  —  The  Disjunctive 
Syllogism  —  The  Dilemma  —  References. 

XIV.  Fallacies  in  Argumentation 141 

What  a  Fallacy  is  —  A  Classification  of  Fallacies  — 
Classification  of  Deductive  Fallacies  —  Fallacies  of  Equivo- 
cation —  Fallacies  of  Unwarranted  Assumption  —  Conclu- 
sion —  References. 

XV.  The  Natube  op  Induction  .' 159 

Induction  and  Deduction  —  A  Glance  at  the  History  of 
Logic  —  The  Function  of  the  Syllogism  —  Why  the  Syl- 
logism is  only  a  Part  of  Reasoning  —  Steps  in  Systematic 
Investigation  —  Three  Elements  in  Investigation  —  The 
Problem  of  Generalization  —  The  Implication  of  Generaliza- 
tion —  How  Generalization  differs  from  Expectation  — The 
Importance  of  Generalization — Testing  Generalizations — 
References. 

XVI.  The  General  Methods  of  Science     .      .      .  173 

•  How  Science  developed  —  The  Need  of  Analysis  —  The 
Value  of  Technique  and  Instruments  —  The  Importance  of 
Measiu-ement  —  Experimentation  —  The  Use  of  Experi- 
ment in  Biology  —  Experimentation  in  Psychology  —  The 
Statistical  Method  —The  Method  of  Graphs  — The  Func- 
tion of  Hypotheses  —  References. 

XVn.  Observation  and  Fact 184 

The  Need  of  Observation  —  The  Difficulty  of  securing 
Data  —  Conditions  of  Accurate  Observation  —  Errors  in 
Perception  —  Causes  of  Erroneous  Perception  —  Summary 
for  Perception  —  Observation  in  Everyday  Life  and  in 
Science  —  Memory  and  Facts  —  Summary  of  Causes  of 
Mistaken  Memory  —  Testimony  —  Facts  differ  in  Differ- 
ent Sciences  —  What  are  Relevant  Facts?  —  References. 

XVIII.  The  Origin  and  Use  of  Hypotheses      .      .  197 

What  is  an  Hypothesis.'  —  Kinds  of  Hypotheses  —  Are 
Hjrpotheses  Necessary  for  Science?  —  The  Origin  of  Hy- 


Yi  CONTENTS 

potheses  —  A  Glance  at  the  Psychology  of  Conjecture  —  The 
Value  of  Hypotheses  —  The  Development  of  an  Hypothesis    . 
— The  Proof  of  an  Hypothesis  —  Fact,  Theory,  and  Hypoth- 
esis —  Analogy  as  a  Basis  of  Reasoning  —  False  Analogy 

—  References. 

XIX.  The  Discovery  and  Proof  of  Causal  Rela- 

tions   211 

How  Experience  comes  to  us — What  are  Causal  Connec- 
tions? —  Post  Hoc  ergo  Propter  Hoc — Mill's  Methods — The 
Method  of  Agreement  —  Examples  of  Induction  by  Agree- 
ment —  The  Character  of  the  Method  —  DiflBculties  con- 
fronting the  Method  —  The  Method  of  Difference  —  Exam- 
ples of  the  Method — Warnings  —  The  Method  of  Concom- 
itant Variations  —  Examples  of  the  Method  —  Warning 

—  The  Joint  Method  of  Agreement  and  Difference  —  Ex- 
amples —  The  Method  of  Residues  —  Examples  —  Re- 
marks on  Mill's  Methods  —  References.  . 

XX.  Statistics .      .      .228 

The  Nature  of  Statistics  —  Stages  in  Statistical  Investi- 
gation —  The  Law  of  Statistical  Regularity  —  Dangers  in 
the  Use  of  Statistics  —  The  Value  of  Statistics  —  Refer- 


XXI.  Probability 289 

Abstract  Laws  vs.  Concrete  Events — Where  Certainty  is 
Possible  —  The  Meaning  of  Probability  —  Probability  and 
Chance  —  Three  Kinds  of  Estimations  —  Empirical,  or  Non- 
Quantitative,  Probability  —  Probabilities  based  on  Averages 
— The  Mathematical  Treatment  of  Probability —  Mistakes 
in  interpreting  Probabilities  —  References. 

XXII.  Averages  and  Graphs 251 

The  Uses  of  Averages  —  The  Arithmetical  Average  — 
The '  Weighted '  Average  —The  Mode —The  Median— The 
Geometric  Average  —  The  Comparative  Advantages  of 
these  Averages  —  Graphs  and  Graphical  Methods  — 
References. 

XXIII.  Testimony  and  Circumstantial  Evidence    .  264 

Scientific  Investigation  vs.  Judicial  Proof  —  The  Difficul- 
ties confronting  Judicial  Proof  —  Distinction  between  Cir- 


CONTENTS  vii 

cumstantial  and  Testimonial  Evidence — The  Nature  of  Cir- 
cumstantial Evidence  —  The  Convergence  of  Evidence  — 
Direct  or  Testimonial  Evidence  —  The  Modern  Critical  At- 
titude' toward  Testimony  —  Logical  Standards  and  Testa 
—  The  Movement  of  Judicial  Proof  —  The  Massing  of 
Mixed  Evidence  —  References. 

XXIV.  Explanation  and  System-Formation       ^      .  278 

The  Nature  of  Explanation  —  The  Sentiment  of  Ration- 
ality —  The  R6le  of  Concepts  —  Proof  and  Explanation  — 
Systems  are  tentative  —  Levels  of  Explanation  —  General 
Explanation  and  Specific  Explanation  —  Typical  Systems 
of  Knowledge  —  References. 

XXV.  Truth  and  its  Tests 294 

Back  to  the  Definition  of  Logic  —  The  Nature  of  Con- 
sistent Thinking  —  The  Laws  of  Thought  —  The  Postu- 
lates of  Logic  —  The  Question  of  Truth  —  The  Criteria  of 
Truth  —  Degrees  of  Belief  —  What  the  Attainment  of 
True  Ideas  implies  —  The  Meaning  of  Truth  —  Truth  and 
the  Will  to  Believe  —  The  Logic  of  Doubt  —  References. 

Questions  and  Exercises 311 

Indsx 345 


THE  ESSENTIALS  OF  LOGIC 

CHAPTER  I 

INTKODUCTORY 

A  Definition  of  Logic.  Logic  may  be  defined  as 

the  science  of  the  principles  and  conditions  of  correct 
thinking.  To  the  beginner,  a  definition  serves  mainly 
as  a  guide-post  to  direct  his  attention  to  the  general 
character  of  the  subject  which  he  is  about  to  study.  The 
above  definition  should  therefore  be  taken  merely  as  an 
indication  of  the  field.  The  terms  of  which  it  is  com- 
posed will  gather  content  and  meaning  as  the  various 
topics  are  covered.  Toward  the  end  of  the  course,  it  is 
to  be  hoped  that  the  student  will  be  able  to  come  back 
to  the  definition  with  a  fuller  grasp  of  its  significance. 
Logic  is  a  science  in  the  sense  that  it  is  organized 
knowledge  involving  principles.  The  various  sciences 
have  different  fields  for  investigation,  but  all  of  them 
agree  in  their  purpose,  which  is  the  establishment  of 
satisfactory  information  bound  together  and  illuminated 
by  laws.  Thus,  physics  studies  the  most  general  charac- 
teristics of  the  physical  world  and  seeks  to  reduce  to 
order  and  interpret  the  facts  it  discovers ;  botany  ex- 
amines the  structures,  functions,  and  histories  of  plants ; 
and  psychology  gives  its  attention  to  the  behavior  of 
creatures  possessing  consciousness.  All  these  sciences 
seek  to  replace  the  loose  and  hazy  notions  of  popular 
thought  by  exact  and  systematic  knowledge.  Now  logic 


2  THE  ESSENTIALS  OF  LOGIC 

has  the  same  purpose,  but  its  field  is  peculiar.  It  can- 
not be  classed  among  the  physical  sciences  which  de- 
pend upon  perception  and  measurement,  nor  among  the 
biological  sciences,  nor,  finally,  among  the  social  sciences. 
In  a  very  real  sense  modem  logic  presupposes  all  these 
sciences  and  is  somehow  a  science  at  second  remove 
from  things.  It  is  a  science  about  the  mental  aspect  of 
the  sciences.  The  mediaeval  logicians  pointed  out  that  the 
mind  first  'intends,'  or  directs  itself  upon,  the  exter- 
nal world,  and  that  only  afterwards  does  it  direct  itself 
upon  the  mental  processes  and  methods  it  has  used.  We 
may  say,  then,  that  logicjnvolves  a  thinking  about 
thinking. 

Because  man  is  naturally  outward-looking  and  de- 
sirous of  practical  results  he  is  seldom  clearly  conscious 
of  his  methods  and  of  the  mental  processes  involved  in 
thinking.  It  requires  an  effort  for  him  to  take  this  new 
attitude  and  to  think  about  thinking,  about  those  mental 
operations  which  make  knowledge  possible.  But  when 
he  does  so,  he  finds  that  the  mind  does  work  in  an 
orderly  fashion.  It  is  the  nature  of  this  orderliness  that 
logic  seeks  to  bring  into  clear  consciousness. 

The  Value  of  Logic.  So  far  as  logic  is  a  pure 
science,  its  value  is  essentially  of  the  same  kind  as  that 
of  any  other  pure  science.  It  satisfies  an  intellectual 
curiosity,  a  desire  to  know.  Before  a  teacher  can  appeal 
strongly  to  such  a  value,  the  student  must  have  expe- 
rienced it;  at  some  past  time  he  must  have  forgotten 
himself  as  an  individual  with  private  ambitions  in  the 
enjoyment  of  seeing  problems  solved,  of  watching  mean- 
ing replace  confusion ;  he  must  have  felt  pleasure  in 
knowledge  for  its  own  sake.  The  logician  who  is  loyal 


mTRODUCTORY  8 

to  his  subject  because  he  has  faith  in  it  asserts  that  logic 
has  a  value  as  a  pure  science,  that  man  likes  to  know 
the  working  of  his  own  mind  just  as  he  likes  to  know 
the  laws  of  celestial  mechanics.  Why  not,  indeed?  Is 
not  the  mind  the  supreme  instrument  which  all  must 
employ? 

But  a  pure  science  need  not  lack  practical  value. 
Logic  is  not  only  a  pure  science,  but  also  an  art  or  an 
applied  science.  An  applied  science  is  one  which  is  able 
to  work  out  suggestions  and  rules  based  on  a  broad  study 
of  the  field  involved.  Looked  at  from  this  angle,  logic 
may  be  considered  "a  free  study  of  some  of  the  chief 
risks  of  error  in  reasoning."  ^  What  logic  can  do  for  an 
individual  is  to  render  him  conscious  of  the  best  meth- 
ods and  the  main  difficulties  in  the  various  stages  of 
actual  thinking  so  that  he  will  be  more  exacting  in  his 
mental  operations.  It  should  put  him  on  his  guard 
against  dangers.  It  calls  his  attention  incessantly  to  the 
value  of  clear  and  unambiguous  ideas  and  to  the  proper 
level  of  scrutiny  to  be  maintained  before  a  fact  is  ac- 
cepted, an  inference  drawn,  or  a  proposition  admitted 
as  a  premise  in  reasoning.  The  mind  is  an  instrument, 
and  it  should  be  polished  instead  of  being  left  in  a  state 
of  nature.  It  is  true  that  the  exigencies  of  life  force  us 
to  be  critical,  but  such  criticism  is  too  rough-and-ready 
to  be  entirely  satisfactory.  Is  there  good  reason  to  doubt 
that  care  of  the  mind  will  pay  at  least  as  much  as  care 
of  the  body?  There  are  good  mental  habits  just  as  there 
are  good  physical  habits;  and  neither  comes  without 
effort  and  reflection.  "Its  [logic's]  practical  value  in 
general  education  is  firstly,  this :  that  it  demands  very 
^  Sidgwick,  Elementary  Logic,  p.  8,  Introduction. 


4  THE  ESSENTIALS  OF  LOGIC 

careful  and  exact  thinking  about  its  own  subject-matter, 
{ind  thus  tends  to  produce  a  habit  of  similar  carefulness 
in  the  study  of  any  other  subject.  In  this  it  only  does 
for  the  mind  what  a  thorough  training  in  any  other 
science  might  do.  Secondly,  it  makes  us  realizejjetter 
what  the  general  forms  of  speech  that  we  habitually  use 
really  mea^,  and  familiarizes  us  with  the  task  of  examin- 
ing our  reasonings  and  looking  to  see  whether  they  are 
jconclu^iye,  In  this  it  has  an  effect  which  the  study  of 
some  special  science  like  botany  is  not  equally  calcu- 
lated to  produce.  Thirdly,  it  brings  into  clearer  con- 
sciousness, as  aforesaid,  our  ideal  of  what  knowing  Js, 
and  so  furnishes  us  withji^Qrtj)f_negatiye_st_andard;  it 
makes  us  more  alive  to  shortcomings  in  our  ordinary 
opinions.  But  its  chief  value  lies  in  its  bearing  upon 
those  ultimate  problems,  concerning  the  nature  of  real- 
ity, and  man's  place  and  destiny  in  the  world,  from 
which  at  first  sight  it  might  seem  far  remote."  ^ 

If  logic  can  do  even  a  part  of  this,  it  justifies  itself 
as  a  practical  study.  While  logic  does  not  create  new 
capacities  in  the  mind  of  an  individual,  it  helps  to  train 
and  sharpen  the  capacities  already  there. 

The  Kinds  of  Logic.  Logic  is  one  of  the  oldest  of 
the  sciences  and  has  had  a  varied  history.  The  result 
has  been  the  growth  of  different  branches  emphasizing 
different  aspects  of  thinking  and  somewhat  different  in- 
terpretations of  the  aim  of  logic.  At  times,  these  '  kinds 
of  logic '  have  seemed  opposed  to  one  another,  but,  of 
late,  they  are  seen  to  supplement  one  another  and  to 
make  logic  a  broader  investigation  than  it  would  have 
beeu  without  this  branching.  One  kind  of  logic  (exact 
'  Joseph,  An  Introduction  to  Logic,  p.  10. 


INTRODUCTORY  5 

or  symbolic)  seeks  to  assimilate  itself  to  mathematics 
in  its  methods ;  another  (concrete)  stresses  its  relation 
to  general  philosophy,  especially  to  theory  of  knowl- 
edge ;  another  (empirical  or  inductive)  lays  its  emphasis 
upon  the  methods  of  the  experimental  and  observational 
sciences.  Back  of  these  historically  and  linking  itself 
with  them  in  various  ways —  sometimes  welcomed,  some- 
times an  outcast  —  is  what  is  called  '  Formal  Logic' 
We  shall  have  a  better  idea  of  the  limitations  of  Formal 
Logic  as  we  cover  various  topics  such  as  the  '  syllogism,' 
'  immediate  inference,'  and  the  '  logical  form '  of  state- 
ments. Certain  doctrines  and  technicalities  must  be  dis- 
cussed and  given  as  true  and  adequate  a  setting  as  pos- 
sible. They  have  their  value,  though  this  value  must 
not  be  overestimated. 

Introductory  Logic.  The  Introductory  Logic  of 
to-day  in  America  seeks  to  organize  together  the  essen- 
tials of  the  various  kinds  of  logic.  It  retains  as  much 
of  Formal  Logic  as  seems  valuable  and  combines  it  with 
a  concreter  study  of  actual  thinking  with  a  view  to  de- 
termine the  principles  and  conditions  of  correct  think- 
ing. In  this  effort,  it  has  been  aided  immensely  by  the 
growth  of  psychology  and  philosophy,  and  the  increasing 
reflection,  by  scientists  themselves,  upon  their  methods. 
Logic  has  acquired  a  new  lease  of  life  and  is  genuinely 
growing.  More  is  known  about  thinking  than  ever  be- 
fore, and  this  added  knowledge  has  stimulated  logic  to 
break  away  from  formalities.  Yet  logic  has  a  rich  in- 
heritance from  the  past  which  must  not  be  belittled. 
What  is  needed  is  a  new  perspective  and  a  more  vital 
setting.  We  want  to  know  the  structure  of  our  actual 
thinking  so  as  to  guard  against  the  risks  of  error. 


6  THE  ESSENTIALS  OF  LOGIC 

Relation  of  Logic  to  Other  Sciences.  The  sciences 
most  closely  related  to  logic  are  rhetoric  and  psychology. 
The  connection  with  psychology  is  obvious  and  we  must 
examine  it  in  some  detail.  But  first  let  us  examine  its 
relation  to  grammar  and  rhetoric. 

Thinking  is  intimatelybound  up  with  language; 
language  is,  in  fact,  a  necessary  instrument  to  any  sus- 
tained thinking  which  involves  general  ideas.  For  gram- 
mar, language  is  itself  the  s^ibject-matter ;  for  logic,  it 
is  the  instrument  of  thought.  The  function  of  words 
is  the  fixation  of  meanings  in  our  own  mind  and  their 
suggestion  to  others.  In  another  chapter  we  shall  discuss 
the  relation  between  thought  and  language.  At  present 
we  only  wish  to  point  out  that  the  law  of  language 
under  its  logical  aspect  is  that  of  non-ambiguity.  State- 
ments must,  so  far  as  possible,  be  clear  as  regards  their 
significance.  Accuracy  and  appropriateness  in  the  use 
of  words  go  hand  in  hand  with  the  discrimination  of 
ideas. 

Rhetoric  is  more  nearly  akin  to  logic  than  is  gram- 
mar. While  grammar  treats  of  words  largely  apart 
from  their  meanings,  rhetoric  concerns  itself  with  the 
expression  of  thought.  Such  expression  is  studied  in 
relation  to  the  purpose  in  hand,  which  may  be  expo- 
sition, description,  argumentation  or  persuasion.  It  is 
impossible  to  draw  any  hard-and-fast  line  between  these 
disciplines,  for  each  is  influenced  by  the  results  of  the 
other;  we  may  say,  however,  that  to-day  both  riietoric 
and  logic  presuppose  grammar  as  a  preliminary  and  dif- 
fer from  each  other  in  that  which  they  stress.  Logic  is 
more  interested  in  the  meaning  which  is  expressed, 
its  implications,  foundation,  and  validity,  than  in  the 


INTRODUCTORY  7 

mode  or  style  in  which  it  is  expressed.  Rhetoric,  on 
the  other  hand,  culminates  Jn  thejjtistic  use  of  lan- 
guage. The  fact  that  language  is  a  necessary  instrument 
of  thought  brings  these  disciplines  together;  but  logic_ 
has  wider  relations  because  thought  is  greater  than  its 
i^trument.  Language  is,  after  all,  a  tool. 

The  logician  reflects  upon  the  mental  processes  by 
means  of  which  knowledge  is  achieved  and  naturally 
finds  much  assistance  in  psychology.  So  far  as  he  in- 
vestigates Aoro  the  individual  thinks  and  the  conditions 
of  this  thinking,  he  works  hand  in  hand  with  the  psy- 
chologist. Both  examine^erceptionLConception,  judg- 
ment  and  reasoning  and  reach  harmonious  conclusions. 
The  main  difference  between  them  is  that  psychology 
concerns  itself  more  with  the  mental  content,  while 
logic  stresses  the  valueof  the  product.  Just  because 
tlie  mind  is  a  unity,  it  is  impossible  to  find  other  than 
a  working  distinction  between  them  due  to  a  division 
of  labor.  They  overlap,  then,  in  the  higher  mental  pro- 
cesses, and  logic  passes  on  to  a  study  of  the  structure 
of  knowledge  and  its  validity,  while  psychology  con- 
cerns itself  with  the  structure  of  consciousness,  its  rela- 
tion to  conduct,  and  its  physiological  conditions  and 
concomitants.  The  logician  has  the  right  to  make  use 
of  the  knowledge  psychology  has  achieved  which  bears 
upon  his  own  task.  Their  relation  should  be  one  of 
mutual  helpfulness. 

The  Material  of  Logic.  All  sciences  are  objective ; 
that  is,  they  consist  of  recognized  facts  and  of  princi- 
ples which  organize  and  interpret  these  facts.  Now, 
logic  is,  as  we  have  already  pointed  out,  a  science  about 
the  sciences.  It  is  interested  in  the  nature  of  proof  and 


8  THE  ESSENTIALS  OF  LOGIC 

\the  laws  of  evidence  ;  it  desires  to  see  how  knowledge 
Us  built  up  and  how  the  parts  of  knowledge  depend 
vupon  one  another.  This  interest  cannot  be  satisfied  by 
introspection  alone,  but  requires  a  close  study  of  the 
various  sciences.  In  these  it  finds  knowledge,  and  in 
their  history  the  record  of  the  steps  by  which  it  was 
obtained.  We  may  say,  then,  that  the  material  of  logic 
is  to  be  found  in  generally  accepted  knowledge  and 
that  this  is  approached  with  the  purpose  of  discovering 
the  processes  involved.  Knowledge  is  the  material  of 
logic  much  as  the  organism  is  the  material  of  the 
biologist  and  the  inorganic  world  the  material  of  the 
physicist. 

Inductive  logic  has  always  paid  close  attention  to  the 
sciences  which  have  so  splendidly  developed  since  the 
Renaissance.  It  is  an  attempt  to  formulate  the  methods 
which  grew  up  unconsciously,  or  largely  unconsciously, 
in  this  new  and  wonderful  extension  of  human  knowl- 
edge. The  assumption  controlling  the  series  of  inves- 
tigations which  have  given  us  the  inductive  branch  of 
logic  has  been  very  well  expressed  by  Whewell :  "  We 
may  best  hope  to  understand  the  nature  and  conditions 
of  real  knowledge  by  studying  the  nature  and  condi- 
tions of  the  most  certain  knowledge  which  we  pos- 
sess ;  and  we  are  most  likely  to  learn  the  best  methods 
of  discovering  truth  by  examining  how  truths,  now  uni- 
versally recognized,  have  really  been  discovered."  ^ 

But  logic  must  concern  itself  with  all  sorts  of  think- 
ing, with  the  conversations  of  daily  life,  with  the  argu- 
ments to  be  found  in  the  social  sciences,  in  political 
speeches,  in  essays,  in  editorials ;  otherwise,  it  is  apt  to 
*  Wbevell,  History  of  Scientific  Ideas  {3d  ed.),Tol.  i,  p.  4. 


INTRODUCTORY  9 

become  too  formal  and  pedantic  and  to  lose  touch  with 
the  flexibility  and  variety  of  actual  thought.  There  is 
another  reason  why  the  logician  puts  this  emphasis  on 
less  specialized  thinking  and  refuses  to  let  it  be  elbowed 
away  by  the  more  technical  levels  of  thought.  We  can 
know  what  thinking  is  only  by  thinking  ourselves  and 
then  retracing  our  steps  in  memory  to  see  exactly  what 
we  have  been  doing.  Thematerial  of  logic  can  be  found 
ultimately  only  in  consciousness.  And,  if  the  subject- 
matter  is  to  be  realized  and  really  reflected  upon,  it 
must  be  reproduced  and  revivified  in  our  own  thought. 
But  it  is  not  always  easy  to  do  this  with  past  thinking 
when  this  is  technical  and  has  an  atmosphere  of  its 
own.  And,  when  all  is  said,  familiar  thinking  illustrates 
the  essentials  of  the  thinking  process.  Any  one  who 
studies  logic  seriously  must  be  willing  to  think  for  him- 
self and  to  think  about  his  thinking. 

REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  I. 
Sigwart,  Logic,  vol.  I,  General  Introduction. 
Joseph,  An  Introduction  to  Logic,  chap.  I. 
Sidgwick,  Elementary  Logic,  Introduction. 
Schiller,  Formal  Logic,  chap.  i. 


CHAPTER  II 

THE  NATURE  AND  SETTING  OF  THOUGHT 

What  is  Thought  ?  Thinking  is  the  central  opera- 
tion for  logic.  It  is  the  operation  which  underlies 
knowledge  and  opinion  and  makes  them  possible.  It 
behooves  us,  therefore,  to  gain  as  clear  an  idea  of  its 
nature  and  conditions  as  we  can.  If  it  is  affected  by 
mental  habits,  we  want  to  know  what  are  the  best  hab- 
its ;  if  it  is  controlled  by  feeling  and  emotion,  we 
want  to  know  how  to  lessen  such  control.  In  short, 
we  wish  to  study  the  ways  in  which  the  human  mind 
assimilates  and  develops  knowledge  —  especially  that 
knowledge  which  is  called  true. 

It  is  not  easy  to  define  that  mental  process  desig- 
nated thinking.  "  No  words  are  oftener  on  our  lips 
than  thinhing  and  thought.  So  profuse  and  varied,  in- 
deed, is  our  use  of  these  words  that  it  is  not  easy  to 
define  just  what  we  mean  by  them.  Assistance  may 
be  had  by  considering  some  typical  ways  in  which  the 
terms  are  employed.  In  the  first  place,  thought  is  used 
broadly,  not  to  say  loosely.  Everything  that  comes 
to  mind,  that  *goes  through  our  heads,'  is  called  a 
thought.  To  think  of  a  thing  is  just  to  be  conscious 
of  it  in  any  way  whatsoever.  Second,  the  term  is  re- 
stricted by  excluding  whatever  is  directly  presented ; 
we  think  (or  think  of)  only  such  things  as  we  do  not 
directly  see,  hear,  smell,  or  taste.  Then,  third,  the 
meaning  is  further  limited  to  beliefs  that  rest  upon 


THE  NATURE  AND  SETTING  OF  THOUGHT    11 

some  kind  of  evidence  or  testimony.  Of  this  third  type, 
two  kinds  —  or,  rather,  two  degrees  —  must  be  dis- 
criminated. In  some  cases,  a  belief  is  accepted  with 
slight  or  almost  no  attempt  to  state  the  grounds  that 
support  it.  In  other  cases,  the  ground  or  basis  for  a 
belief  is  deliberately  sought  and  its  adequacy  to  sup- 
port the  belief  examined.  This  process  is  called  reflec- 
tive thought."  ^  Now,  logic  is  chiefly  interested  in  this 
higher  level  of  thinking  where  ideas  are  under  control 
and  organized  in  relation  to  one  another.  In  fact,  many 
logicians  define  logic  as  the  science  of  proof  or  evidenc^. 

Certain  terms  are  used  by  logicians  as  practically 
synonymous.  Thus  we  shall  have  occasion  to  speak  of 
reflective  thought^  reasoning^  and  inference  at  various 
times.  These  processes  are  much  the  same,  though  the 
context  will  show  slight  differences  of  emphasis.  Tak- 
ing them  as  essentially  the  same,  our  present  task  is  to 
find  out  what  is  the  nature  of  the  mental  operation 
involved.  What  do  we  do  when  we  reason  or  infer? 
What  we  want  now  is  a  suggestion  of  the  general  char- 
acter of  the  operation,  leaving  it  to  later  chapters  to 
study  the  various  steps  in  methodical  reasoning. 

Discovery  and  Proof.  There  are  two  parts  to  any 
complete  act  of  reasoning,  discovery,  and  proof.  We 
reason  when  we  are  confronted  by  problems,  by  unfore- 
seen situations  to  which  our  habits  and  usual  ideas 
are  not  immediately  applicable.  We  are,  as  we  say,  at 
a  loss ;  we  don't  know  what  to  think  or  to  do.  But  this 
perplexity  lasts  for  a  time  only.  We  make  shift  to  size 
up  the  situation,  to  compare  it  with  what  in  the  past 
seems  most  like  it,  to  analyze  the  various  features,  and 

1  Dewey,  How  We  Think,  pp.  1-2. 


12  THE  ESSENTIALS  OF  LOGIC 

so  on,  until  some  idea  suggests  itself  as  a  possible  solu- 
tion. Such  is  the  stage  of  tentative  discovery.  But 
another  stage  immediately  sets  in.  The  suggested  solu- 
tion must  be  tested  or  proved.  In  practical  affairs,  this 
proving  consists,  in  the  main,  of  overt  action.  The 
new  idea  is  tried  out  to  see  whether  it  will  work.  The 
proud  possessor  of  a  new  auto  finds  himself  compelled 
to  reason  in  this  rough-and-ready  way  only  too  often. 
This  practical  level  of  reasoning  is  sometimes  called 
*  trial-and-error.'  The  process  is  familiar  to  all. 
..  In  more  theoretical  reasoning,  both  the  stage  of  dis- 
covery and  the  stage  of  proof  are  reflective.  The  sci- 
entist who  makes  a  discovery  has,  as  a  rule,  long 
brooded  over  the  problem.  The  idea  of  universal  gravi- 
tation did  not  come  to  Newton  as  a  mere  chance 
thought ;  his  mind  was  ripe  for  it.  Archimedes  had 
long  been  pondering  over  his  particular  problem  before 
he  took  his  famous  bath  and  discovered  the  principle  of 
specific  gravity.  But  after  the  brilliant  idea  has  sug- 
gested itself,  it  must  be  proved  in  the  light  of  the  facts. 
It  must  be  shown  to  follow  from  certain  premises  or 
data ;  it  must  be  guaranteed  by  its  reasons  or  grounds. 
And  this  second  task  is  often  the  more  perplexing  of 
the  two.  By  proof  wejaean^  the  process  of  ^tablishing 
an  idea  on  a  firm  intellectual  foundation.  Newton  had 
to  work  out  the  method  of  fluxions  and  make  delicate 
calculations  on  the  basis  of  known  measurements  before 
he  could  consider  his  hypothesis  reasonably  proved, 
while  Darwin  had  to  make  numerous  experiments  and 
collect  data  of  the  most  varied  kinds  before  he  was 
willing  to  publish  his  theory.  Proof  must  be  considered 
a  very  important  part  of  reasoning.  Scrupulousness  in 


THE  NATURE  AND  SETTING  OF  THOUGHT    13 

regard  to  its  standards  is  the  sign  of  a  trained  mind. 
It  is  not  too  much  to  say  that  logic  is  primarily  the 
science  of  proof.  The  question  before  the  logician's 
miud  is,  '  Is  such  and  such  a  given  conclusion  war- 
ranted ? '  Logic  is  retrospective  and  probative. 

The  Psychologist's  Vie"w  of  Reasoning.  In  the 
preceding  chapter,  we  came  to  the  conclusion  that  logic 
and  psychology  overlap,  that  no  hard-and-fast  line  can 
be  drawn  between  them.  It  may  be  of  interest,  there- 
fore, to  examine  the  psychologist's  view  of  reasoning. 
"To  define  reasoning  fully  it  must  be  distinguished 
from  imagination  and  memory  when  observed  from  the 
inside,  and  from  instinct  and  habit  when  expressed  in 
action.  Reasoning  may  be  distinguished  from  memory 
and  imagination,  not  so  much  by  the  character  of  the 
mental  states  or  by  the  way  that  they  are  obtained, 
as  by  the  attitude  that  is  taken  toward  them  when  they 
arise.  The  idea  that  is  attained  by  reasoning  may  be 
exactly  like  an  idea  that  on  other  occasions  or  by 
another  man  is  merely  remembered.  The  laws  that 
govern  the  appearance  of  rational  ideas  are  the  laws  of 
association,  controlled  in  the  same  way  as  in  memory 
and  imagination.  The  important  differences  are :  that 
the  results  of  reasoning  are  new  and  are  accepted  as 
true ;  the  results  of  memory  are  true^  but  not  new ; 
and  the  results  of  imagination  are  new^  hut  not  true^  ^ 
It  is  well  to  bear  these  contrasts  in  mind.  Reasoning  is 
a  mental  process  taking  some  time  to  occur  and  con- 
trolled by  the  purpose  of  reaching  accepted  results. 
The  logician  makes  the  further  demand  that  these  re- 
sults be  established  by  relation  to  their  ground. 
*  Pillsbury,  Essentials  of  Psychology,  p.  217. 


14  THE  ESSENTIALS  OF  LOGIC 

Examples  of  Reasoning.  Let  us  take  a  case  of 
reasoning  in  regard  to  heavenly  phenomena  which  was 
made  quite  early  in  the  history  of  civilization.  Man 
soon  discovered  that  a  shadow  was  caused  by  the  inter- 
vention of  an  opaque  body  between  a  source  of  light 
and  a  distant  surface.  He  did  not  know  exactly  what 
took  place,  but  he  knew  that  the  light  was  cut  off  from 
the  region  back  of  the  opaque  body.  Thus  he  arrived 
at  the  universal  proposition,  '  All  shadows  are  caused 
by  the  intervention  of  an  opaque  body.'  But  an  eclipse 
was  soon  recognized  to  be  a  case  of  shadow.  Hence  an 
opaque  body  must  have  intervened  between  the  earth 
and  the  source  of  light.  Here  is  a  case  of  reasoning  in 
which  the  conclusion  is  reached  by  resemblance  or  anal- 
ogy. An  eclipse  is  a  case  of  the  intervention  of  an 
opaque  body  because  it  is  a  case  of  shadow.  This 
reasoning  contains  the  ground.  Let  us  now  examine  a 
case  of  bad  reasoning.  "  According  to  some  accounts, 
the  wise  men  of  Spain  argued  with  Columbus  that  he 
could  not  reach  India  by  sailing  west,  because  if  the 
earth  were  round,  as  he  asserted,  he  would  at  some 
time  reach  a  point  where  the  ship  would  be  going  down- 
hill and  ultimately  fall  off,  just  as  a  minature  vessel 
would  fall,  if  it  should  attempt  to  travel  around  an 
artificial  globe.  If  A  is  true  (earth  round),  B  must  be 
true  (circumnavigation  impossible).  If  there  is  a  re- 
semblance between  earth  and  artificial  globe  in  contour 
of  surface,  there  must  be  a  further  resemblance,  so  it 
was  held,  in  the  relation  of  each  to  the  objects  upon 
its  surface.  ...  In  making  their  comparison,  the  wise 
men  overlooked  an  important  point  of  difference,  viz., 
that  for  an  object  on  the  artificial  globe  the  point 


THE  NATURE  AND  SETTING  OF  THOUGHT    15 

towards  which  it  gravitates  is  outside  the  globe,  while 
for  objects  on  the  earth  this  point  is  within  the  earth 
itself."! 

Thinking  may  be  more  or  less  conscious  and  more  or 
less  methodical.  Logic  seeks  to  induce  individuals  to 
take  thinking  seriously,  to  make  their  thinking  method- 
ical and  reflective.  Especially  does  it  stress  evidence. 
Reflective  thought  is  careful,  and  evidence-loving.  It 
notes  all  the  facts  which  can  be  thought  to  have  bear- 
ing upon  the  problem  and  tests  any  conclusion  by  its 
consequences. 

The  Conditions  and  Occasions  of  Thought.  He- 
flective  thought  or  reasoning  rests  upon  and  grows  out 
of  experience.  It  has  its  causes  and  conditions.  Thought 
does  not  arise  just  for  no  reason  at  all,  but  has  its 
definite  conditions.  These  reasons  for  thinking  can  be 
classified  as  social  and  personal. 

The  stimuli  which  lead  individuals  to  think  usually 
come  from  the  social  environment.  The  pity  is  that 
this  environment  is  so  moderately  stimulating.  The 
more  there  is  the  spirit  of  intellectual  and  social  adven- 
ture, the  more  alive  will  men  be.  When  the  environ- 
ment favors  tradition  and  mere  repetition  and  imitation, 
comparatively  little  vital  and  creative  thinking  is  done. 
Life  takes  on  the  aspect  of  routine  and  habit,  and 
classification  of  a  formal  kind  overshadows  discovery. 
Actions  are  repeated  in  the  customary  grooves,  and  no 
attempt  is  made  to  better  them.  There  are  periods,  as 
during  certain  parts  of  the  Middle  Ages,  when  this 
social  attitude  is  largely  dominant.  At  such  times,  be- 
liefs are  handed  down  by  tradition  and  are  not  criti- 
*  Bode,  An  Outline  of  Logic,  pp.  2-3, 


16  THE  ESSENTIALS  OF  LOGIC 

cally  examined.  Such  an  atmosphere  is  not  favorable 
to  thinking.  The  individual  is  not  taught  to  analyze 
and  observe,  to  doubt  and  to  form  hypotheses.  Thus, 
there  is  a  sociology  of  logic,  or,  rather,  logic  has  its 
social  aspects  which  must  not  be  lost  sight  of.  Let  me, 
by  means  of  an  example,  contrast  the  lethargy  of  thought 
during  the  later  Middle  Ages  with  the  eager  spirit  of 
science  at  its  best. 

It  is  said  that  Francesco  Sizzi,  a  Florentine  astrono- 
mer, argued  against  Galileo's  discovery  of  a  new  planet 
in  the  following  way :  — 

"  There  are  seven  windows  in  the  head :  two  nostrils, 
two  eyes,  two  ears,  and  a  mouth ;  so  in  the  heavens 
there  are  two  favorable  stars,  two  unpropitious,  two 
luminaries,  and  Mercury  alone  undecided  and  indiffer- 
ent. From  which  and  many  other  similar  phenomena 
of  nature,  such  as  the  seven  metals,  etc.,  which  it  were 
tedious  to  enumerate,  we  gather  that  the  number  of 
planets  is  necessarily  seven. 

"  Moreover,  the  satellites  are  invisible  to  the  naked 
eye,  and  therefore  can  have  no  influence  on  the  earth, 
and  therefore  would  be  useless,  and  therefore  do  not 
exist. 

"  Besides,  the  Jews  and  other  ancient  nations  as  well 
as  modem  Europeans  have  adopted  the  division  of  the 
week  into  seven  days  and  have  named  them  from  the 
seven  planets ;  now,  if  we  increase  the  number  of  the 
planets  this  whole  system  falls  to  the  ground."  ^ 

The  present  is,  on  the  whole,  a  period  of  skepticism 
and  inquiry.  The  individual  is  taught  to  think  for  him- 
self, along  certain  lines  at  least,  and  not  to  accept  ideas 
^  Lodge,  Pioneers  of  Science,  p.  106. 


THE  NATURE  AND  SETTING  OF  THOUGHT    17 

unless  he  has  pretty  assured  evidence  for  them.  This 
social  atmosphere,  encouraging  to  thought,  is  a  very 
important  condition  of  thinking.  Logic  has  a  perfect 
right  to  champion  such  conditions.  It  is  not  called 
upon  to  be  a  passive  judge  of  consistency  alone. 

The  personal  conditions  of  thought  are  also  impor- 
tant. The  prime  condition  is  the  recognition  of  a  prob- 
lem. Back  of  this  recognition  lies  the  attitude  which 
faces  problems  and  even  goes  to  meet  them  halfway. 
This  attitude  is  partly  temperamental,  partly  the  con- 
sequence of  training.  On  the  practical  side  of  life,  so 
long  as  our  habitual  ways  of  acting  are  sufficient  to 
meet  the  conditions  which  confront  us,  there  is  little 
reflective  thought  because  there  is  little  need  for  it. 
There  is  mental  activity,  of  course,  because  we  must 
constantly  recognize  and  classify  things  and  situations ; 
but  this  classificatory  interpretation  is  usually  so  im- 
mediate that  the  individual  does  not  need  to  pause,  or, 
if  he  does  pause,  it  is  only  for  a  moment.  Difficulties 
arise,  however,  frequently  enough,  and  the  course  of 
action  is  stayed.  New  adjustments  must  be  worked 
out,  and  these  adjustments  depend  upon  the  proper 
location  of  the  difficulty  and  the  discovery  of  its  nature 
and  remedy.  Thinking  intervenes  at  such  a  time.  It 
is  the  sign  and  consequence  of  uncertainty,  doubt,  in- 
ability to  interpret.  How  successfully  the  individual 
meets  the  problem  depends  upon  his  training,  capacity, 
and  character. 

The  Setting  of  Thought.  Thinking  arises  and 
takes  its  coui'se  in  the  mind  of  an  individual  endowed 
with  a  fund  of  past  experiences.  The  problem  which 
occasions  thinking  involves  a  conflict  within  experi- 


18  THE  ESSENTIALS  OF  LOGIC 

ence  and  calls  into  play  all  that  is  in  any  way  relevant. 
Familiar  ideas,  prejudices,  habits,  memories,  all  enter 
into  the  council-chamber  and  demand  audience.  Think- 
ing is  tiie  individuaFs  experience  in  process  of  intftrng^l 
adjustment. 

We  may  say,  then,  that  thinking  is  purposive  and 
selective.  It  is  an  expression  of  the  growth  of  the 
mind.  But  the  mind  is  distorted  by  old  beliefs  and 
prejudices  and  is  very  frequently  deflected  from  the 
truth.  It  is  like  a  river  whose  banks  throw  the  current 
from  side  to  side  and  produce  in  it  all  sorts  of  treach- 
erous eddies.  The  logician  must  do  the  work  of  an 
engineer.  He  must  point  out  the  dangers  which  con- 
front the  mind  which  desires  to  think  truly. 

Why  we  think.  Our  study  of  the  conditions  and 
setting  of  thought  enables  us  to  answer  the  question, 
'  Why  do  we  think  ?  '  There  is  both  a  practical  and  a 
theoretical  urgency  behind  thought.  Life  demands  that 
problems  be  solved  in  order  that  we  may  act  wisely. 
When  our  habits  push  us  in  different  directions,  we 
must  work  out  some  suggestion  which  satisfies  our  mind 
or  we  are  distraught.  Besides,  we  know  from  past  ex- 
perience how  dangerous  it  is  to  trust  to  a  chance  idea. 
We  want  to  have  a  fair  degree  of  assurance  of  the  con- 
sequences before  we  act.  To  think  is  to  rehearse  the 
course  of  events  beforehand  and  to  meet  every  emer- 
gency with  its  appropriate  interpretation. 

But  psychologists  inform  us  that  it  is  the  very  nature 
of  the  mind  to  work  out  harmonious  ideas.  The  things 
we  see  are  the  products  of  adjustments.  However  far 
down  we  go  in  our  mental  life,  we  find  the  endeavor 
to  harmonize  various  elements  with  one  another.  "  The 


THE  NATURE  AND  SETTING  OF  THOUGHT    19 

sensations  that  are  received  are  added  to  or  changed  to 
make  them  correspond  more  exactly  to  what  from  our 
different  earlier  experiences  we  know  they  must  be. 
One  always  corrects  the  shape  of  the  table-top  as  it 
appears  in  perspective.  The  angles  are  right  angles  as 
we  see  them,  although  the  image  must  have  acute  and 
obtuse  angles.  One  always  makes  an  allowance  for  dis- 
tance in  the  size  of  an  object  that  is  seen.  The  same 
object  is  always  given  the  same  size  no  matter  how  far 
away  it  may  be,  while  the  image  on  the  retina  dimin- 
ishes constantly  as  the  distance  increases."  ^  Thus,  pro- 
cesses of  adjustment  are  characteristic  of  the  mental 
life  at  its  different  levels.  This  same  tendency  ex- 
presses itself  in  thinking.  Thinking  arises  naturally 
and  inevitably  when  the  adjustment  cannot  be  made 
almost  automatically. 

We  have  stressed  practical  problems  as  an  explana- 
tion of  thought;  but  theoretical  problems  are,  at  the 
present  day,  as  fruitful  in  thought.  These  two  types 
of  problems  are  intimately  interwoven  by  the  very  na- 
ture of  life,  for  there  are  few  ideas  which  do  not  have 
a  bearing  upon  conduct.  Yet  the  interests  involved 
are  fairly  distinguishable.  The  growth  of  science  has 
assisted  man  to  develop  interests  of  an  impersonal 
kind,  and  about  these  interests  and  the  investigations 
connected  with  them  arise  theoretical  problems.  Facts 
must  be  interpreted  by  theories  and  these  theories 
must  be  harmonized  so  far  as  possible.  The  trained 
human  mind  is  not  satisfied  with  disorder  and  contra- 
diction ;  it  seeks  to  bring  harmony  out  of  chaos  and  to 
organize  its  ideas  into  a  harmonious  whole.  Conflict  in 
^  Pillflbury,  Essentials  of  Psychology,  p.  157. 


20  THE  ESSENTIALS  OF  LOGIC 

any  realm  is  to  such  a  mind  a  stimulus  to  thought.  The 
piocess  of  thinking  has  back  of  it  all  the  forces  and 
habits  which  demand  order.  To  say  that  man  is  ra- 
tional is  to  say  that  he  seeks  adjustment  among  his 
ideas. 

Processes  preliminary  to  Reflective  Thought. 
The  processes  preliminary  to  reflective  thought  are, 
roughly  speaking,  two :  perception  and  conception.  We 
must  have  percepts  and  the  ideas  formed  from  them 
before  we  can  think.  Together,  they  furnish  the  ma- 
terial within  which  thinking  goes  on.  It  must  not 
be  supposed .  that  percepts  and  concepts  (ideas)  are 
given  apart  from  mental  activity,  but  it  is  true  to  say 
that  the  higher  mental  processes,  such  as  judging,  ana- 
lyzing, drawing  conclusions,  and  argumentation,  occur 
within  a  field  of  experience  already  fairly  stable  and 
definite.  We  see  the  external  world,  recognize  various 
familiar  objects  in  it,  know  what  to  expect  of  them, 
and  have  a  pretty  generous  fund  of  ideas  when  we  are 
engaged  in  the  solution  of  any  particular  problem. 
The  individual's  mind  is  constantly  adding  to  its  store 
of  information  and  its  working  system  of  distinctions, 
classification,  and  expectations.  It  is  correct,  then,  to 
say  that  thinking  represents  the  growing  point  of  the 
mind,  and  that  it  leaves  a  sediment,  so  to  speak,  of 
ideas  and  habits  and  points  of  view.  We  must  remem- 
ber, however,  that  any  part  of  this  accepted  knowledge 
may  be  challenged  by  new  problems  and  new  experi- 
ences ;  hence  we  must  think  of  the  mind  as  a  living 
organism  rather  than  as  a  building  in  which  one  story 
is  added  to  another. 

The  psychologist  has  much  to  teU  us  of  sensations,  of 


THE  NATURE  AND  SETTING  OF  THOUGHT    21 

their  qualities  and  intensities  and  number.  This  infor- 
mation does  not  have  much  bearing  upon  the  subject- 
matter  of  logic,  interesting  as  it  is  in  itself.  We  know 
that  the  sense  organs  must  be  stimulated  before  we  can 
have  these  sensations  with  which,  in  the  rough  and  un- 
analyzed,  we  are  all  of  us  familiar.  The  next  level  after 
sensation  is  perception.  It  is  of  advantage  to  the  logi- 
cian to  realize  that  perception  is  a  complex  process  and 
that  the  percepts  which  we  have  as  a  result  may  be 
partly  false.  Whenever  there  is  possibility  of  error,  the 
logician  cannot  be  indifferent.  When  we  come  to  a 
study  of  scientific  method,  we  shall  have  considerable  to 
say  about  errors  in  observation.  A  few  words  about  the 
general  character  of  percepts  and  perception  may  not 
be  amiss  at  this  point. 

Put  technically,  percepts  are  the  mental  objects 
which  result  from  the  interpretation  of  sensory  stimuli 
by  centrally  aroused  processes.  They  are  the  primary 
mental  objects  of  which  we  are  aware  when  we  use  our 
senses.  There  is  a  sensory  basis  in  all  percepts ;  but 
there  is,  furthermore,  a  large  element  of  applied  past 
experience.  A  percept  is  really  a  mental  product  to  the 
making  of  which  there  has  gone  much  trial,  selection, 
and  adjustment.  The  cumulative  result  of  these  proc- 
esses is  given  as  an  object,  while  the  processes  them- 
selves seldom  appear  in  consciousness.  So  far  as  more 
is  given  in  the  2)erc€pt  than  the  senses  warrant,  the 
logician  speaJcs  of  the  inferential  element  in  percep- 
tion. It  is  because  of  this  inferential  element  that  per- 
ceptions may  be  erroneous.  We  may  see  things  which 
aie  not  present  because  we  take  a  certain  sensory  cue 
and  add  to  it  qualities  which  often  have  accompanied  it 


22 


THE  ESSENTIALS  OF  LOGIC 


in  our  experience.  What  we  shall  unconsciously  add  de- 
pends largely  upon  the  setting  and  upon  the  ideas  which 
are  occupying  our  minds.  The  following  examples  may 
make  this  possibility  of  error  in  perception  more  evident. 
In  the  following  figure  taken  from  Jastrow,  one  can 
actually  see  dim  lines  suggested  by  the  heavy  lines  that 
are  drawn.  These  are  supplied  by  memory.^ 

£DJTOH 

This  second  figure  may  be  seen  as  a  rabbit's  head  or 
as  a  duck's  according  to  the  thought  which  is  upper- 
most.2 


I  Jastrow,  Fact  and  Fable  in  Psychology,  Fig.  2.        '^  Ibid.,  Fig.  19. 


THE  NATURE  AND  SETTING  OF  THOUGHT    23 

These  illusions  as  they  are  called,  serve  to  bring  out 
the  amount  of  interpretation  which  is  at  work  in  every- 
day life.  Here  is  another  example :  "  If  a  sportsman, 
while  shooting  woodcock  in  cover,  sees  a  bird  about  the 
size  and  color  of  a  woodcock  get  up  and  fly  through  the 
foliage,  not  having  time  to  see  more  than  that  it  is  a 
bird  of  such  a  size  and  color,  he  immediately  supplies 
by  inference  the  other  qualities  of  a  woodcock,  and  is 
afterwards  disgusted  to  find  that  he  has  shot  a  thrush. 
I  have  done  so  myself,  and  could  hardly  believe  that  the 
thrush  was  the  bird  I  had  fired  at,  so  complete  was  my 
mental  supplement  to  my  visual  perception."  ^ 

Speaking  of  such  illusions,  William  James  says: 
*' Twenty  times  a  day  the  lover,  perambulating  the 
streets  with  his  preoccupied  fancy,  will  think  he  per- 
ceives his  idol's  bonnet  before  him." 

Conception  arises  upon  perception  as  a  foundation. 
Concrete,  perceived  objects  are  dissected  into  elements, 
and  these  elements,  loosened  from  their  particular  con- 
text, are  capable  of  repeated  recall.  Concepts  are  men- 
tal objects  which  are  (1)  not  directly  connected  with 
the  stimulation  of  sense-organs,  and  (2)  are  under  our 
control  so  far  as  our  having  or  riot  having  them  is  con- 
cerned. The  mental  processes  which  make  concepts 
possible  are  analysis  and  abstraction  assisted  by  the 
method  of  comparison.  We  note  the  likenesses  and  dif- 
ferences between  things.  Certain  qualities  begin  to  stand 
out  and  are  selected  by  the  attention.    These  quali- 

^  Romanea,  Mental  Evolution  in  Animals,  p.  324. 

^  The  student  \rill  find  James's  discussions  of  illusions  extremely  in- 
teresting, especially  pages  95  to  103  of  the  second  volume  of  the  Prin- 
ciples of  Psychology.  Miinsterberg's  On  the  Witness  Stand,  chap,  i,  is  also 
augfgestive. 


24  THE  ESSENTIALS  OF  LOGIC 

ties  and  relations  are  then  abstracted  or  considered  by 
themselves,  while  the  other  features  of  the  thing  are 
disregarded.  The  result  of  this  analysis  is  the  isolation 
of  the  quality  or  relation  from  its  context  and  our 
ability  to  recall  it  again  and  again  at  need.  Such  ab- 
stracted, repeatable  mental  objects  are  called  '  con- 
cepts.' Other  terms,  sometimes  employed,  are  '  mean- 
ings,' '  ideas,'  '  universals.'  This  last  term  stands  for  a 
species  of  concept  which  is  of  special  interest  to  the 
logician,  and  frequently  used  in  philosophy.  A  universal 
is  a  concept  which  applies  to  an  indefinite  number  of 
individual  things.  Any  class  name  is  a  good  example 
of  a  universal.  We  all  have  the  idea  of  a  horse,  of  an 
auto,  of  a  soldier,  etc.  Such  ideas  are  universals. 

The  ability  to  form  concepts  is  essential  to  reason- 
ing and  reflective  thought  in  general.  Conceptual  ele- 
ments, obtained  by  comparison  and  abstraction,  are 
organized  together  in  all  sorts  of  ways.  Only  by  means 
of  concepts  are  we  able  to  rise  above  the  particular  field 
of  concrete  perception  spread  out  before  our  senses. 
Knowledge  is  primarily  an  affair  of  conception,  of  rules 
and  principles,  facts  and  theories.  But  it  must  not  be 
forgotten  that  these  elements  work  back  into  and  con- 
trol our  interpretation  of  the  world  we  see  about  us. 
There  is  a  constant  and  responsible  interplay  of  per- 
ception and  conception  in  our  minds.  Logic  concerns 
itself  with  this  interplay  so  far  as  it  can  be  made  the 
object  of  a  critical  reflection. 

Fact  and  Theory.  The  distinction  between  percept 
and  concept  is  more  characteristic  of  psychology  than 
of  logic.  For  the  latter,  the  more  distinctive  contrast  is 
between  fact  and  theory.  In  any  argument,  we  con- 


THE  NATURE  AND  SETTING  OF  THOUGHT    25 

stantly  seek  to  separate  what  may  be  considered  the 
facts  of  the  case  from  the  theory  which  is  added  to  it  as 
an  interpretation.  Argument  and  dispute  arise  where 
fact  and  theory  are  not  clearly  separated  ;  and  the  first 
step  to  the  settlement  of  the  argument  is  an  agreement 
as  to  what  is  fact  and  what  is  theory.  Now,  fact  is  that 
which  is  admitted  for  the  purpose  of  the  argument ;  it 
is  that  which  is,  temporarily  at  least,  considered  indis- 
putable. And  it  is  interesting  to  note  that  fact  in  this 
sense  may  be  either  concrete  or  abstract.  The  Law  of 
Gravitation  is  a  fact  because  it  is  an  assertion  which  I 
do  not  question.  A  theory,  on  the  other  hand,  is  that 
which  is  tentative  and  disputable.  It  needs  support, 
proof,  corroboration. 

The  first  step  in  reflective  thought  or  argument  is, 
therefore,  to  distinguish  fact  from  theory,  the  indisputa- 
ble from  the  disputable.  "  In  practice,  assertions  are 
seldom  or  never  wholly  untrue,  especially  when  they 
correspond  to  a  genuine  belief.  It  is  sometimes  difficult, 
but  seldom  impossible  (if  it  be  thought  worth  while),  to 
find  a  basis  of  agreement  even  with  those  whose  view 
seems  most  opposed  to  our  own.  Some  part  of  the  way 
they  go  with  us,  and  then  the  roads  branch  off.  Why 
did  they  leave  our  road,  or  why  did  we  leave  theirs  ? 
That  question  and  its  answer  is  the  beginning  of  argu- 
ment. The  matter  of  argument  is  always  matter  of 
opinion ;  not  fact  but  theory ;  not  fact  but  inference 
from  fact."  ^ 

Kno\7ledge  a  Growth.  No  problem  or  doubt  which 
gives  rise  to  reflective  thought  challenges  all  the  indi- 
vidual's world.  There  is  always  fact  as  well  as  theory, 
1  Sidgwick,  The  Process  of  Argument,  p.  18. 


26  THE  ESSENTIALS  OF  LOGIC 

the  accepted  as  well  as  the  disputed.  Knowledge  is  a 
growth  and,  like  every  growth,  has  a  structure  of  its 
own.  Logic  has  to  pay  considerable  attention  to  the 
structure  of  knowledge  and  its  medium,  language.  If 
argument  is  knowledge  in  the  making^  it  would  seem 
impossible  to  understand  it  apart  from  pretty  adequate 
ideas  of  what  knowledge  as  made  consists  in.  All 
through  logic,  then,  we  see  process  and  product,  growth 
and  achievement,  dovetailed  together.  It  is  really  im- 
possible to  understand  one  apart  from  the  other.  All 
problems  arise  within  the  knowledge  already  attained 
and  reflect  its  structure.  This  fact  explains  why  logic 
has  to  take  up  so  many  topics  which  seem  linguistic 
or  concern  themselves  with  the  divisions,  classifica- 
tions, and  distinctions  in  knowledge  rather  than  with 
discovery,  argument,  and  reasoning. 

REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  i. 

Bosanquet,  The  Essentials  of  Logic,  Lecture  n. 

Dewey,  How  We  Think,  chap.  I. 

Pillsbury,  Essentials  of  Psychology,  chaps,  vil  and  IX. 

James,  Principles  of  Psychology,  vol.  ii,  chap.  xxii. 


CHAPTER  III 

ABOUT  TERMS 

The  Unit  of  Thought.  The  logician  considers  the 
judgment  or  the  proposition  as  the  unit  of  thought. 
The  conclusion  of  a  vital  act  of  thought  may  find  ex- 
pression in  a  proposition,  but  in  nothing  short  of  it. 
Thus,  in  answer  to  a  friend's  question,  I  may  say  that  a 
certain  man  is  reliable;  but  I  cannot  use  the  words 
'  man '  and  '  reliable  '  in  isolation  and  convey  any  as- 
sured meaning.  The  unit  of  thought  is  a  complex  idea, 
which  is  asserted  or  denied.  Since  thinking  arises  under 
the  stimulus  of  a  problem,  its  result  must  be  definite, 
it  must  assert  or  deny  something.  This  definite  solution 
of  a  problem  is  called  a  '  judgment '  and  its  verbal  form 
a  '  proposition.' 

The  proposition  can  be  analyzed  into  elements  which 
are  called  '  terms.'  These  terms  exhibit  the  complexity 
of  the  proposition,  and  are  always  present  in  a  relation 
characteristic  of  the  concrete  act  of  thought.  '  Fire 
bums,'  'Justice  is  kingly,'  are  propositions  in  which 
there  is  both  unity  and  complexity,  or,  better  yet,  unity 
in  complexity.  In  trying  to  understand  the  judgment, 
we  must  carefully  distinguish  between  the  mental  proc- 
ess of  thinking  which  finds  its  goal  in  an  accepted  idea 
and  the  accepted  idea  itself.  It  is  this  latter  which  finds 
expression  in  the  proposition  and  which  is  analyzed  by 
the  logician. 

The  Elements  of  the  Proposition.  A  proposition 
is  always  analyzable  into  a  subject  and  a  predicate.  The 


28  THE  ESSENTIALS  OF  LOGIC 

subject  is  that  about  which  something  is  stated,  while 
the  predicate  is  that  which  is  stated  about  the  subject. 
These  two  elements  are  called  the  *  subject  term '  and 
the  ♦  predicate  term '  respectively.  And  this  brings  us 
to  the  definition  of  a  'logical  term.'  It  is  any  word  or 
group  of  words  which  can  serve  as  the  subject  or  the 
predicate  of  a  proposition.  But  these  two  terms  do  not 
exhaust  the  proposition.  There  is,  further,  the  word 
which  stands  for  the  relation  between  these  terms.  This 
is  called  the  '  copula.'  In  the  proposition,  '  Abraham 
Lincoln  was  a  wise  statesman,'  the  subject  term  con- 
sists of  two  words  and  is  a  proper  name,  the  predicate 
term  contains  three  words,  while  the  copula  is  a  form 
of  the  verb  '  to  be.' 

Words  and  Terms.  It  should  be  noted  that  the 
different  parts  of  speech  are  not  equally  capable  of 
acting  as  terms  or  as  the  nucleus  of  terms.  Nouns,  pro- 
nouns, verbs,  and  adjectives  have  the  character  or  func- 
tion which  enables  them  to  act  as  the  essential  part 
of  a  term  or  even  as  a  term.  Such  words  are  called 
*  categorematic '  or  asserting  words.  Other  words  are 
not  able  to  designate  an  object  of  thought,  but  are  sub- 
sidiary to  such  designation.  They  are  called  '  syn cate- 
gorematic' Adverbs,  conjunctions,  and  prepositions 
are  connective  or  qualifying  words,  and  are  therefore 
classed  as  syncategorematic. 

Since  terms  often  consist  of  many  words  grouped  to- 
gether, categorematic  words  may  be  found  combined 
together  by  means  of  syncategorematic  words.  In  the 
proposition,  '  Justice  is  hingly  though  no  king  he  just,* 
the  words  italicized  are  categorematic,  while  the  others 
are  syncategorematic.  This  distinction  is,  perhaps,  more 


ABOUT  TERMS  29 

grammatical  than  logical ;  but  it  serves  to  stress  the  fact 
that  a  logical  term  is  other  than  a  word. 

Kinds  of  Terms.  Terms  faU  into  different  classes 
according  to  the  point  of  view  that  is  dominant.  The 
first  division  is  into  '  concrete '  and  '  abstract.'  Concrete 
terms,  again,  are  divided  into  singular  or  individual, 
general  or  class,  and  collective  terms.  Let  us  examine 
these  divisions,  which  are  the  most  important,  before 
glancing  at  other  kinds  of  terms. 

An  abstract  term  is  the  name  of  a  quality  or  rela- 
tion taken  apart  from  its  setting.  In  the  study  of  con- 
ception, the  nature  of  abstraction  was  referred  to.  To 
abstract  is  to  draw  off  or  take  away.  But  an  abstract 
term  is  not  simply  a  word  which  calls  up  an  idea  which 
is  conceptual  in  character,  for  all  words  do  this,  it  is 
a  word  which  signifies  an  attribute  or  relation  taken 
apart  from  any  individual  object.  It  is  the  relation  of 
the  idea  to  realities  which  are  thing-like  which  is  disre- 
garded. Thus,  '  sweetness '  is  an  abstract  term  because 
it  signifies  a  conceptual  object  obtained  by  abstract- 
ing a  quality  of  physical  things  and  considering  it  by 
itself.  The  objects  signified  by  abstract  terms  cannot 
possibly  be  perceived. 

Some  abstract  terms  are  farther  from  sense-percep- 
tion than  are  others.  This  is  because  the  objects  of  which 
they  are  characteristics  involve  more  construction.  Thus, 
'equality,'  *  animality,'  *  constitutionality,'  'discipline,' 
are  abstract  terms  at  second  remove,  so  to  speak.  It  is 
to  be  noted  that  abstract  terms  are  always  nouns. 

A  few  words  need  to  be  said  concerning  the  dangers 
involved  in  the  use  of  abstract  terms.  Since  they  are 
nouns,  they  are  readily  thought  of  as  referring  to  indi- 


30  THE  ESSENTIALS  OF  LOGIC 

vidual  things,  more  subtle  than  physical  things,  yet 
somehow  real  after  the  same  fashion.  The  result  is  a 
fallacy  which  is  usually  called  the  '  fallacy  of  hyposta- 
tization.'  Other  writers  speak  of  it  as  the  '  fallacy  of 
abstract  terms.'  It  consists  of  treating  abstractions  as 
veritable  things.  "  Our  everyday  use  of  such  terms  as 
'  conscience,'  '  memory,'  and  '  will '  shows  further  how 
ingrained  is  this  habit  of  treating  abstractions  as  though 
they  were  independent  things.  In  reality  these  terms 
are  the  names  of  attributes.  It  is  not  uncommon,  how- 
ever, to  find  that  conscience,  for  example,  is  conceived, 
in  a  vague  fashion,  as  though  it  were  some  kind  of  thing, 
inhabiting  the  inmost  recesses  of  the  soul  and  perform- 
ing the  functions  of  an  oracle.  Similarly,  there  is  no 
separate  thing  called  memory  or  will,  but  only  different 
instances  of  remembering  and  willing."  i 

In  contrast  to  an  abstract  term,  a  concrete  term  is  a 
word  or  group  of  words  which  refers  to  a  person  or 
a  thing,  or  a  group  of  persons  or  things.  If  there  is 
any  doubt  whether  a  given  term  is  abstract  or  concrete, 
the  test  to  apply  is,  '  What  does  it  lead  us  to  think  of  ? ' 
If  it  lead  us  to  think  about  definite  individuals,  it  is 
concrete ;  if  it  lead  us  to  think  about  attributes,  it  is 
abstract.  Thus,  *  man,'  '  animal,'  '  a  society,'  '  Lake 
Michigan,'  '  a  red  apple '  are  concrete  terms ;  '  hu- 
manity,' '  animality,'  '  society,'  '  redness '  are  abstract. 

Concrete  terms,  we  have  said,  are  divisible  into  sin- 
gular, general,  and  collective.  These  terms  agree  in  their 
function  of  calling  to  mind  things ;  they  differ  in  the 
number  of  things  implied  and  in  the  way  they  are  taken. 

A  singular  or  individual  term  is  one  which  applies 
*  Bode,  An  Outline  of  Logic,  p.  49. 


ABOUT  TERMS  81 

to  only  one  thing.  Such  a  term  is  selective  and  is  used 
to  identify,  or  direct  our  thoughts  to  a  thing  or  expe- 
rience which  is  regarded  as  a  distinct  existence.  Ex- 
amples :  '  the  large  dictionary  in  this  room,'  '  the  center 
of  the  earth,'  '  the  fifth  page  of  this  book.' 

It  should  be  noted  that  the  point  of  view  determines 
in  large  measure  what  shall  be  regarded  as  a  single 
thing.  A  note  of  music  may  awaken  an  interest  which 
leads  to  a  selective  emphasis  on  it  so  that  it  stands  out 
from  its  setting,  or  it  may  be  completely  merged  in  the 
whole  composition.  It  is  worth  while  to  reflect  upon  this 
relativity  of  what  we  shall  consider  a  thing  to  our  inter- 
est. We  cut  out  things  from  continuous  wholes  much  as 
the  housewife  cuts  out  cookies  from  the  pastry.  We 
divide  up  the  world  into  larger  or  smaller  parts  in  ac- 
cordance with  what  attracts  our  attention.  A  mountain  is 
a  thing,  so  is  a  boulder  on  its  summit,  so  is  a  peculiarly 
colored  portion  of  the  boulder,  so  is,  perhaps,  a  molecule 
in  it,  etc.  A  singular  term  helps  the  individual  to  carry 
on  this  process  of  selective  analysis,  and  enables  him  to 
direct  the  thoughts  of  another  person  to  the  same  goal. 

There  are  two  methods  for  the  formation  of  singular 
terms.  The  first  method  consists  in  the  taking  of  a  term 
which  applies  equally  well  to  many  things  and  adding 
new  words  until  the  application  is  obviously  limited  to 
one  thing  alone.  The  definite  article  always  indicates 
the  singular  term.  Very  often  the  presence  of  the  super- 
lative form  of  an  adjective  or  adverb  helps  to  carry  out 
this  process  of  narrowing  the  application  of  the  term  to 
one  thing.  Examples :  '  the  greatest  politician  in  the 
United  States  to-day,'  '  the  man  who  ran  fastest  in  the 
meet.'  The  second  method  is  to  adopt  a  term  arbitrarily 


82  THE  ESSENTIALS  OF  LOGIC 

as  a  sign  of  a  particular  individual.  Since  language 
is  social,  a  social  element  enters  here.  This  use  of  the 
term  must  be  consented  to  by  the  group.  Personal 
names  are  of  this  character.  Individuals  are  christened 
according  to  a  socially  recognized  procedure.  One  is 
called  *  Bernard  Shaw  ' ;  another,  *  William  Smith ' ; 
another,  *  If-Christ-had-not-died-you-would-have-been- 
damned  Barebones.'  It  is  interesting  to  note  that  a 
personal  name  is  not  always  sufficient  to  select  the  one 
person  meant.  In  that  case,  some  descriptive  word  or 
words  must  be  added.  We  all  remember  the  '  Fiddler 
Smiths '  and  '  Little  John  Petersens '  of  our  boyhood. 

A  general  term  is  one  which  applies  to  any  number 
of  things.  General  terms  are  names  of  kinds  or  classes. 
Grammar  makes  the  distinction  between  common  and 
proper  nouns  which  corresponds  to  a  difference  of  nu- 
merical application.  Examples  of  general  terms  are, 
*  dog,'  '  member  of  Congress,'  '  citizens  of  the  United 
States,'  'holidays.' 

The  objects  covered  by  a  general  term  are  members 
of  a  class.  Such  objects  agree  in  certain  characteris- 
tics and  are  classed  together  because  of  this  agreement. 
These  points  of  resemblance  are  called  '  attributes '  of 
the  class.  It  should  be  noted  that  all  objects  have  some- 
thing in  common,  and  that  the  number  of  possible  classes 
is  infinite.  In  both  practical  life  and  science,  kinds  or 
groups  of  objects  having  very  much  in  common,  are 
worked  out  and  established  as  a  matter  of  general  knowl- 
edge. Such  classes  have  accepted  names.  *  Salts,'  '  halo- 
gens,' '  acids,'  '  vertebrates,'  '  mollusks,'  '  constitutional 
monarchies,'  '  fruits,'  etc.,  are  names  of  well-understood 
classes. 


ABOUT  TERMS  3S 

We  shall  have  occasion  to  consider  class  names  again 
when  we  come  to  the  distinction  between  '  denotation  * 
and  'connotation.'  We  shall  see  that  general  terms  have 
two  functions ;  they  denote  the  individuals  to  which  they 
apply  and  they  connote  the  attributes  which  they  imply. 

Collective  terms  are  a  special  class  of  concrete  terms. 
They  arise  from  the  ability  the  human  mind  has  of 
grouping  objects  together  and  considering  them  in  their 
collective  aspect.  A  collective  term  is  one  which  applies 
to  a  group  of  objects  in  which  the  individual  m,embers 
are  lost  sight  of  in  the  whole.  Such  terms  may  be 
either  singular  or  general.  Examples  of  singular  collec- 
tives are,  '  the  American  navy,'  '  the  crowd  before  the 
courthouse,'  '  the  woman's  club. '  '  Navy,'  '  family,' 
*  tribe,'  '  state,'  *  teacher's  association,'  are  general  col- 
lectives. 

When  we  are  referring  to  some  specific  group,  the 
term  is  employed  as  a  singular.  '  The  American  navy 
is  fairly  efficient.'  '  This  crowd  of  students  is  out  for  a 
good  time.'  A  general  collective  is  used  as  a  general 
term  on  the  ground  that  there  are  various  groups  with 
the  same  characteristics.  It  is  used  distrihutively  of  the 
particular  groups  covered  and  collectively  of  the  mem- 
bers of  any  one  group.  '  Excited  mobs  are  dangerous.* 
'  Woman's  clubs  are  becoming  social  centers.'  This  dis- 
tinction will  become  clearer  when  we  take  up  '  conno- 
tation '  and  '  denotation.'  It  is  necessary  to  go  beyond 
the  mere  form  of  the  words  to  what  is  thought  of  in 
order  to  distinguish  between  singular  and  general  col- 
lectives. 

Ambiguity  sometimes  arises  from  the  fact  that  the 
Eng;lish  word  '  all '  is  used  both  distrihutively  and  col- 


S4  THE  ESSENTIALS  OF  LOGIC 

lectively.  "That  is,  it  may  mean  'all  taken  together' 
or  '  each  and  every.'  Thus,  we  can  say :  '  All  the  angles 
of  a  triangle  are  less  than  two  right  angles,'  and  '  All 
the  angles  of  a  triangle  are  equal  to  two  right  angles.' 
In  the  former  sentence,  the  word  '  all '  is  used  distribu- 
tively,  in  the  latter  collectively.  In  Latin  two  different 
words  are  used :  cuncti  expresses  the  collective  sense  of 
*  all,'  and  omnes  its  distributive  signification."  ^ 

Other  Kinds  of  Terms.  We  have  defined  and  ex- 
amined abstract,  concrete,  singular,  general,  and  collec- 
tive terms.  But  terms  are  divided  from  other  points  of 
view  into  '  absolute  '  and  '  relative,'  and  into  '  positive,' 
'negative,'  and  'privative'  terms.  These  distinctions 
are  significant  enough  to  justify  some  consideration. 

An  absolute  term  is  one  which  refers  to  an  object 
or  quality  considered  by  itself.  The  supposition  is  that 
such  an  object  of  thought  has  meaning  in  its  own  right ; 
it  does  not  depend  on  its  relation  to  something  else  for 
an  essential  part  of  its  meaning.  Thus,  '  stone,'  '  build- 
ing,' '  the  State  of  Michigan '  are  absolute  terms.  A 
relative  term  is  one  which  derives  an  essential  part  of 
its  meaning  from  its  relation  to  something  else.  Ex- 
amples of  relative  terms  are,  '  shepherd,'  '  patient,* 
'  ruler,'  '  citizen,'  '  pupil.'  Relative  terms  usually  go  in 
pairs  which  imply  one  another  and  are  then  called  '  cor- 
relatives.' Thus,  '  teacher '  implies  '  pupils '  and  '  par- 
ent '  implies  '  child  ' ;  and  the  reverse  is  also  the  case. 

It  is  sometimes  said  that  all  things  are  relative  in  the 
sense  that  they  are  interdependent.  This  is  true,  yet  it 
does  not  invalidate  the  logical  distinction  we  have  just 
discussed.  At  the  level  of  common  sense,  we  usually 

^  Creighton,  An  Introductory  Logic,  p.  51. 


ABOUT  TERMS  86 

ignore  the  relations  which  bind  things  to  one  another 
because  they  do  not  come  out  in  perception.  Only  when 
relations  stand  out  so  clearly  that  they  cannot  be  dis- 
regarded, do  they  form  an  essential  part  of  our  thought. 
Man  is  absolute,  but  a  man  as  a  teacher  is  relative. 
This  term  stresses  a  relation  into  which  a  man  may 
enter. 

But  the  term  '  relative '  is  sometimes  used  in  another 
sense.  A  word  may  involve  a  standard.  'Goodness,' 
♦  badness,'  '  luxury,'  '  poverty,'  '  beautiful,'  and  '  slow- 
ness '  are  examples  of  relatives  of  this  kind.  The  danger 
lies  in  the  fact  that  the  standard  is  variable  from  per- 
son to  person,  from  class  to  class  in  society,  and  from 
period  to  period  in  history.  This  variability,  when  not 
recognized,  is  a  fruitful  source  of  confusion.  "To  rec- 
ognize and  point  out  this  character  of  relativity  may 
on  occasion  serve  to  forestall  much  fruitless  argument. 
For  example,  the  question  may  be  asked,  'Are  the 
people  of  the  present  day  more  moral  than  those  of  the 
past  ?  '  Before  we  undertake  to  express  an  opinion  we 
should  ascertain  what  is  meant  by  '  more  moral.'  To 
judge  the  past  by  present-day  standards  is  one  thing: 
to  judge  it  by  its  own  standards  is  quite  another.  Again, 
the  question  may  be  raised  whether  or  not  students  who 
go  into  business  are,  as  a  rule,  more  capable  than  those 
who  adopt  the  profession  of  teaching.  Discussions  of  a 
question  like  this  are  prone  to  overlook  the  relativity  of 
a  phrase  like  '  more  capable.'  Until  we  specify  whether 
we  mean  '  capable  for  business  '  or  '  capable  for  teach- 
ing '  or  some  other  form  of  capableness,  argument  is 
likely  to  be  futile."  ^  The  teacher  in  social  ethics  is 
^  Bode,  An  Outline  of  Logic,  p.  46. 


86  THE  ESSENTIALS  OF  LOGIC 

hound  to  meet  questions  which  turn  around  the  estab- 
lishment of  Sifair  standard  for  such  things  as  expendi- 
ture. And  this  term  '  fair '  is  itself  obviously  a  relative 
term. 

The  distinction  between  positive  and  negative  terms  is 
obvious  enough.  A  positive  term,  is  one  which  implies 
the  presence  of  a  quality  or  qualities.  Thus,  *  efficient,' 
'  selfish,'  '  happy,'  and  '  heavy '  are  positive  terms.  A 
negative  term  is  one  which  implies  the  absence  of 
such  qualities.  '  Inefficiency,'  '  disloyal,'  '  unselfish ' 
are  negative  terms.  In  the  English  language,  such  pre- 
fixes and  suffixes  as  '  un,'  '  in,'  '  dis,'  '  a,'  and  '  less '  are 
used  to  form  negative  from  positive  terras.  It  should  be 
noted  that  contrast-pairs  formed  in  this  way  do  not  box 
the  compass.  Take,  for  example,  the  terms  '  patient ' 
and  '  impatient '  ;  a  man  may  not  be  exactly  patient 
while  he  is  still  far  from  impatient.  The  logician  must 
call  attention  to  this  fact,  however  trivial  it  may  seem, 
because  words  shift  their  meanings.  When  we  come  to 
study  the  possible  manipulations  of  a  proposition,  such 
as  obversion,  we  shall  see  why  it  is  necessary  to  deter- 
mine the  exact  opposite  of  a  term.  *  Intemperate '  is  not 
the  contradictory  of  '  temperate.'  A  little  reflection  and 
some  care  in  the  use  of  words  are  all  that  is  needed. 
Attention  should  be  called  to  another  point.  Too  much 
stress  should  not  be  laid  upon  the  mere  form  of  words. 
It  is  always  best  to  penetrate  to  the  meaning.  Thus, 
such  terms  as  '  invaluable '  and  '  unloosed  '  are  positive 
in  their  meaning,  while  it  seems  nonsense  to  speak  of 
'  intemperance '  as  negative.  The  absence  of  one  quality 
means  the  presence  of  a  condition  just  as  positive.  The 
negative  form  is  an  accident  of  language  in  such  cases. 


ABOUT  TERMS  87 

For  the  sake  of  completeness,  we  referred  to  the  class 
of  privative  terms.  A  privative  term  is  one  which  sig- 
nifies the  absence  of  a  quality  which  is  usually  present. 
Because  of  the  importance  of  this  lack  to  which  they- 
refer,  they  are  positive  in  form.  Examples :  '  maimed,' 
'  deaf,'  '  blind,'  '  orphaned.' 

Connotation  and  Denotation.  General  or  class 
terms  have  two  functions:  they  apply  to  the  members 
of  the  class  and  they  serve  to  recall  the  common  attri- 
butes of  the  class.  Thus  the  term  does  double  duty :  it 
enables  us  to  bear  individual  things  in  mind  while 
thinking  of  them  as  belonging  to  a  class,  and  it  is  a  sign 
of  the  essential  attributes  of  the  class. 

This  double  function  of  class  terms  reflects  the  way 
in  which  such  terms  develop.  We  notice  that  certain 
things  have  points  of  similarity,  and,  if  these  common 
qualities  are  important  to  us,  we  group  these  things  to- 
gether and  think  of  them  largely  in  terms  of  their  com- 
mon qualities.  As  a  matter  of  fact,  we  never  think  of 
the  things  without  some  thought  of  the  qualities,  nor  of 
the  qualities  without  the  implicit  assumption  that  they 
are  possessed  by  things.  We  may  say,  then,  that  deno- 
tation and  connotation  go  together  just  as  inevitably  as 
do  qualities  and  things.  They  are  the  reflection  into  the 
class  term  of  this  natural  and  constant  distinction.  It 
is  for  this  reason  that  general  terms  denote  things  and 
connote  qualities. 

Synon3mis  for  Connotation  and  Denotation. 
Instead  of  '  denotation,'  some  logicians  speak  of  the  '  ex- 
tension '  or  *  scope '  of  the  term.  The  corresponding 
names  for  '  connotation  '  are  '  mtension '  and  '  compre- 
hension.' '  Denotation '  and  '  connotation  '  are  prefer- 


38  THE  ESSENTIALS  OF  LOGIC 

able  because  they  have  the  verb  forms,  '  denote  and 
'  connote,'  and  the  adjective  forms,  '  denotative '  and 
'  connotative.' 

The  Inverse  Variation  of  Connotation  and  De- 
notation. The  wider  or  higher  the  class,  the  fewer  the 
attributes  which  the  members  of  the  class  have  in  com- 
mon. As  you  pass  from  a  species  to  a  genus  in  biology, 
the  number  of  animals  or  plants  covered  by  the  term 
ii)creases  while  the  common  attributes  decrease  in  num- 
ber. This  double  fact  is  summarized  by  saying  that  de- 
notation and  connotation  vary  inversely.  This  variation 
does  not,  however,  follow  any  mathematical  law.  In- 
crease the  number  of  qualities  possessed  in  common, 
that  is,  widen  the  connotation,  and  the  members  of  the 
class  possessing  these  qualities  will  be  fewer  in  number. 
The  following  series  will  illustrate  this  principle  :  '  man,' 
*  Americans,'  '  Americans  of  European  descent,' '  native- 
born  Americans,'  '  native-born  Americans  who  are  citi- 
zens of  Michigan,'  etc. 

It  should  be  noted  that,  in  our  actual  thinking,  the 
connotation  of  a  term  is  more  apt  to  be  explicit  than 
the  denotation.  We  do  not  actually  run  over  the  various 
members  of  the  class,  but,  instead,  have  some  individual 
vaguely  in  mind  as  a  specimen. 

Terms  and  Meaning.  AU  words  have  meaning. 
This  meaning  varies  from  the  most  substantive  and 
definite  to  the  most  fugitive  and  fluctuating.  The  mean- 
ing of  a  word  is  inseparable  from  the  context  in  which 
it  is  used.  It  is  for  this  reason  that  both  the  logician 
and  the  psychologist  hold  that  the  sentence  or  even  the 
paragraph  is  the  lowest  unit  of  thought.  A  word  or  a 
group  of  words  constitutes  a  term,  and  this  term  has  a 


ABOUT  TERMS  39 

complex  meaning.  It  is,  however,  best  to  distinguish  be- 
tween the  meaning  of  a  term  and  connotation.  In  the 
first  place,  the  distinction  between  denotation  and  conno- 
tation comes  out  clearly  only  for  class  terms;  in  the  second 
place,  the  meaning  of  a  class  term  includes  both  its  de- 
notation and  its  connotation.  We  mean  the  objects  we 
think  of  as  well  as  the  qualities  they  have  in  common. 

REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  rv. 
Creighton,  An  Introductory  Logic,  chap.  rv. 
Joseph,  An  Introduction  to  Logic,  chap.  n. 
Sobiller,  Formal  Logic,  chap.  n. 


CHAPTER  rV 

THE  USE  AND  MISUSE  OP  LANGUAGE 

The  Necessity  for  Language.  Logic  deals  with 
thinking  and  with  knowledge  which  is  the  resultant  of 
thinking.  But  thought  is  impossible  without  language. 
It  is  for  this  reason  that  logic  has  to  concern  itself  so 
fully  with  language  and  its  relation  to  thought.  "  Lan- 
guage is  not  merely  an  accompaniment  of  ideational 
activity ;  it  is  an  instrument  essential  to  its  develop- 
ment. It  is  an  appropriate  means  of  fixing  attention 
upon  ideally  represented  objects  as  distinguished  from 
percepts.  It  becomes  the  more  necessary  the  more  ab- 
stract ideal  representation  is,  —  in  other  words,  the  less 
it  contains  of  the  concrete  details  of  actual  sense-per- 
ception. .  .  .  Within  the  mind  of  the  individual  thinker 
it  serves  to  fix  attention  on  the  object  of  his  own  ideas ; 
in  communication  with  others,  it  serves  to  fix  the  atten- 
tion of  the  hearer  on  the  ideally  represented  objects 
present  to  the  mind  of  the  speaker."  i  As  we  advance 
in  our  study  of  logic,  we  shall  realize,  ever  more  clearly, 
what  an  intimate  part  language  plays.  Systematic 
knowledge  is  bound  up  with  the  use  of  a  definite  set 
of  symbols,  though  these  symbols  may  be  of  various 
kinds.  Each  special  science  works  out  its  own  technical 
terms,  while  mathematics  has  advanced  step  by  step 
with  its  notation. 

Language  and  Analysis.   In  a  preceding  chapter  ^ 

^  Stout,  Manual  of  Psychology,  p.  462. 

2  Chapter  n,  "  The  Nature  and  Setting  of  Thought." 


THE  USE  AND  MISUSE  OF  LANGUAGE      41 

we  suggested  that  reasoning  is  based  upon  the  percep- 
tion of  likeness  and  difference.  Now,  language  assists 
such  discrimination  by  giving  names  to  the  common 
factors  and  aiding  in  their  recall  and  free  manipulation 
apart  from  perception.  Gradually  a  world  of  ideas  is 
built  up  in  which  man  may  freely  move.  Words  are 
the  means  by  which  such  ideas  are  fixated.  It  has  been 
proved  by  experiment  that  we  both  observe  and  remem- 
ber features  of  our  experience  better  if  we  possess 
words  to  attach  to  them. 

The  Logical  La'^v  of  Language.  The  logical  law 
of  language  is  non-ambiguity.  Actually,  words  are  in- 
definite and  misty  on  their  edges.  We  use  them  in  a 
rough-and-ready  fashion.  We  feel  their  appropriateness 
and  develop  habits  in  their  use.  The  consequence  is 
that  there  is  not  enough  delicacy  in  discrimination ;  we 
tend  to  class  things  together  when  we  notice  that  they 
have  common  features.  Yet  the  differences  may  be  of 
more  significance  for  the  problem  in  hand  than  the 
similarities. 

The  neglect  of  relevant  distinctions,  when  these  are 
important  Jar  clear  thinking  or  adequate  statement,  is 
ambiguity.  The  ideal  of  the  logician  is  to  encourage 
individuals  in  those  mental  habits  of  accuracy  and  dis- 
crimination which  are  calculated  to  prevent  ambiguity. 
The  logical  law  of  language  is  non-ambiguity,  an  ideal 
to  which  we  should  approach  ever  more  nearly. 

Causes  of  Ambiguity.  There  are  many  causes  of 
ambiguity,  but  the  basic  cause  is  mental.  Ideas  are 
allowed  to  remain  vague,  and,  as  a  consequence,  they 
overlap  and  get  into  one  another's  way.  Just  as  things 
are  often  classed  roughly  together  because  their  differ- 


42  THE  ESSENTIALS  OF  LOGIC 

ences  are  not  noted,  so  ideas  are  only  too  frequently 
merged  and  confused.  But  clear  and  accurate  thinking 
depends  as  much  upon  the  awareness  of  differences  as 
upon  the  awareness  of  similarities.  Only  he  who  is 
willing  to  take  the  trouble  to  distinguish  things  and 
ideas  which  are  ordinarily  grouped  roughly  together, 
can  escape  the  pitfall  of  ambiguity. 

But  ambiguity  has  a  social  significance.  Incorrect 
and  inadequate  thinking  when  expressed  in  language 
appears  as  ambiguous  statements  and  arguments.  Such 
statements  are  apt  to  deceive  the  unwary  because  they 
also  refuse  to  make  an  analysis  of  the  ideas  involved. 
Hence  ambiguities  tend  to  propagate  themselves  and 
father  a  series  of  fallacies. 

Now,  while  unwillingness  or  inability  to  analyze  the 
various  fields  of  experience,  in  order  to  build  up  clear- 
cut  ideas  not  easily  confused,  is  the  basic  cause  of  ambi- 
guity, there  are  other  causes  at  work,  the  variation  of 
the  meaning  of  words  with  the  purpose  or  general  con- 
text, and  the  imperfections  of  language  as  an  instru- 
ment. It  is  difficult  for  language  to  keep  pace  with  the 
subtlety  and  flexibility  of  thought.  It  is  so  easy  to  sub- 
stitute the  average  meaning  for  the  particular  meaning 
which  the  situation  demands.  Again,  a  word  may  have, 
and  usually  does  have,  more  than  one  meaning  of  an 
average  sort ;  and,  to  make  matters  worse,  words  are 
constantly  changing  their  meanings.  We  always  have 
more  ideas  than  words  with  which  to  express  them.  It 
may  be  said  that  this  ability  of  a  single  word  to  do  duty 
for  more  than  one  idea  is  a  perfection  rather  than  an 
imperfection,  but  it  certainly  brings  its  dangers.  A 
sharp  eye  for  the  context  or  purpose  is  the  main  safe- 


THE  USE  AND  MISUSE  OF  LANGUAGE      43 

guard.  If  this  is  not  obvious  to  the  reader  or  listener, 
ambiguity  is  unavoidable. 

Univocal  Words.  Words  which  have  only  one 
meaning  are  called  '  univocal.'  The  best  examples  of 
univocal  words  are  to  be  found  in  the  technical  terms 
of  the  special  sciences.  In  these,  a  term  is  adopted,  or 
made,  as  an  accepted  sign  of  a  definite  idea  reached  by 
painstaking  investigation.  Consequently,  the  danger  of 
ambiguity  is  at  a  minimum.  To  secure  such  carefully 
delimited  ideas  is  one  of  the  chief  purposes  of  any  sci- 
ence ;  it  is  a  recognized  condition  of  advance.  The 
technical  terms  of  a  special  science  when  taken  together 
form  its  nomenclature.  Thus,  '  molecule,'  *  electron,' 
'  vertebrate,'  '  cell,'  *  angle '  are  technical  terms.  It 
should,  however,  be  noted  that  not  all  technical  terms 
are  strictly  univocal ;  it  is  only  when  they  are  given  in 
the  context  of  their  special  field  that  they  have  but  one 
meaning.  But  this  context  is  easily  recognized. 

Equivocal  Words.  Words  which  have  more  than 
one  meaning  are  'equivocal.'  The  vast  majority  of 
words  which  do  not  apply  to  material  things  are  equiv- 
ocal, as  can  be  seen  by  glancing  over  the  columns  of 
any  large  dictionary.  Thus,  to  take  a  simple  word  like 
'stop,'  we  find  that  it  means  (1)  'to  close,'  (2)  'to 
confine,'  (3)  '  to  arrest,'  (4)  '  to  interrupt.'  Besides 
these  popular  uses,  it  has  technical  meanings  in  music, 
ihetoric,  optics,  horticulture,  and  finance.  It  is  no  won- 
der that  a  foreigner  has  difficulty  in  learning  another 
language,  and  I  am  sure  that,  if  all  the  humorous 
stories  told  in  this  connection  are  not  true,  at  least 
there  is  ground  for  most  of  them.  The  truth  is  that 
there  are  not  enough  words  to  go  around,  and  we  are 


44  THE  ESSENTIALS  OF  LOGIC 

obliged  to  make  one  word  do  the  duty  of  many.  A  per- 
ception of  the  setting  is  essential  if  ambiguity  is  to  be 
avoided.  The  only  practical  advice  the  logician  can 
offer  is  to  seek  for  the  particular  meaning  and  not  trust 
the  average  or  general  meaning  of  the  term. 

Words  change  their  Meanings.  There  are  several 
tendencies  at  work  to  change  the  meanings  of  words. 
The  three  most  important  are  generalization,  specializa- 
tion, and  transfer  of  meaning  by  association  and  analogy. 

At  first,  a  word  is  the  sign  of  a  concrete  thing  or 
class  of  things.  It  is  later  extended  to  all  those  things 
which  have  a  conspicuous  attribute  in  common.  As  time 
goes  on,  extensions  to  more  abstract  objects  take  place. 
This  change  of  application  from  a  concrete  particular 
to  analogous  things  and  objects  of  thought  is  called 
'  generalization.'  "  The  word  '  law '  has  undergone  ex- 
pansion under  the  pressure  of  physical  research.  Reg- 
ularity, uniformity,  constancy  of  occurrence  is  a  much 
wider  idea  than  bare  authoritative  prescription  enforc- 
ing obedience  under  the  threat  of  punishment — which 
is  the  simple  juridical  conception."  ^  How  easily  ambi- 
guity arises  when  two  meanings  coexist  can  be  seen 
from  the  following  quotation :  "  The  existence  of  a 
power  is  even  implied  in  the  phrase  '  laws  of  nature,' 
constantly  used  by  science ;  for  wherever  there  is  a  law 
there  must  be  a  lawgiver,  and  the  lawgiver  must  be 
presumed  capable  of  suspending  the  operation  of  law."  2 
Another  instance  of  this  ambiguity  of  the  word  law 
has  come  to  light  in  recent  discussions  bearing  upon 
the  nature  of  '  international  law.'  The  English  word 

*  Davidson,  The  Logic,  of  Definition,  p.  5. 

^  Goldwin  Smith,  Guesses  at  the  Middle  of  Existence,  p.  143. 


THE  USE  AND  MISUSE  OF  LANGUAGE       45 

'  law '  translates  what  is  expressed  in  continental  tongues 
by  two  words ;  in  German  by  recht  and  gesetz,  in  French 
by  droit  and  loi.  Is  there  an  international  law?  If  we 
mean  by  'law,'  gesetz  and  loi,  no  ;  if  we  mean  recht  and 
droit,  yes.  It  is  obvious  that  we  have  too  few  words  in 
such  a  case. 

Other  simpler  examples  of  this  principle  of  general- 
ization are  '  fluid,'  '  acid,' '  curve,'  and  '  oval.'  We  pass 
from  the  particular  to  the  more  general  and  abstract. 

Again,  words  may  take  on  a  more  special  meaning. 

*  Priest,'  '  minister,'  '  captain,'  '  clerk '  are  examples  of 
this  tendency  to  select  a  special  application  of  the  more 
general  meaning  and  to  ignore  the  other  meanings.  One 
of  the  most  interesting  cases  of  this  specialization  which 
has  led  to  ambiguity  is  the  word  '  prove.'  Originally  it 
meant  '  to  test '  as  in  the  saying,  "  The  exception  proves 
the  rule."  Now  it  means  '  to  test  successfully.'  I  pre- 
sume that  many  a  one  has  wondered  how  the  exception 
could  prove  the  rule. 

There  is,  finally,  the  tendency  to  transfer  a  word  to 
analogous  or  associated  objects.  Thus,  the  word '  church* 
is  used  to  designate  the  religious  body,  the  building,  and 
some  temporary  group  of  worshipers.  We  speak  of  the 

*  chair '  when  we  mean  the  presiding  officer,  or  of  the 

*  bench '  when  we  mean  the  judiciary.  It  would  be 
right  to  list  under  this  heading  those  epithets  which  are 
based  on  felt  analogies.  Such  epithets  startle  the  mind 
and  force  it  to  recognize  similarities  which  would  other- 
wise have  passed  unnoticed.  It  is  the  poet,  with  his 
keen  sensing  of  likenesses  and  differences,  who  is  most 
apt  to  bring  far-removed  aspects  of  experience  together 
by  an  illuminating  phrase.  We  feel  the  appropriateness 


46  THE  ESSENTIALS  OF  LOGIC 

of  the  expression  while  we  hesitate  to  analyze  it,  so 
subtle  and  elusive  is  the  connection. 

These  classes  of  changes  in  the  meanings  of  words 
make  us  realize  what  a  complex  instrument  language  is. 
It  is  necessary  to  know  all  the  essential  meanings  of 
commonly  used  words  and  to  have  some  idea  of  how 
new  shades  of  significance  are  added. 

Vagueness.  Vagueness  is  often  the  cause  of  ambi- 
guity, but  it  is  not  the  same  as  ambiguity.  Our  ideas 
of  the  meanings  of  the  words  we  use  may  be  hazy,  but, 
so  long  as  the  subject  we  are  talking  or  thinking  about 
is  simple,  this  lack  of  definiteness  in  our  ideas  may  not 
lead  us  astray.  So  long  as  the  problem  is  general  and 
relatively  practical,  no  great  measure  of  analysis  is 
needed.  We  must  remember  that  words  are  frequently 
used  just  to  indicate  things  and  to  suggest  plans  of  ac- 
tion and  desirable  attitudes.  Thus,  common  nouns  are 
seldom  used  incorrectly  even  though  the  majority  of 
people  would  be  hard  put  to  it  to  give  an  exact  defini- 
tion. Yet,  even  here,  there  is  doubt  when  those  excep- 
tional cases  are  met  which  fall  on  the  dividing-line  be- 
tween two  classes.  Is  this  man  a  doctor  or  a  quack?  Is 
this  lawyer  a  genuine  lawyer  or  a  pettifogger  ?  The 
trouble  is,  of  course,  not  so  much  one  of  language  as  of 
classification.  Classes  shade  into  one  another  and  their 
edges  are  blurred.  Accuracy  and  completeness  of  classi- 
fication are  the  pre-conditions  of  clear  ideas. 

The  reason  for  vagueness  in  the  understanding  and 
application  of  words  can  partly  be  traced  to  the  method 
by  means  of  which  the  individual's  vocabulary  is  devel- 
oped. Words  are  picked  up  in  their  special  applications 
and  then  extended  to  what  are  judged  to  be  similar 


THE  USE  AND  MISUSE  OF  LANGUAGE      47 

cases.  "  The  mode  in  which  words  are  learned  and  ex- 
tended may  be  studied  most  simply  in  the  nursery.  A 
child,  say,  has  learnt  to  say  '  mambro '  when  it  sees  its 
nurse.  The  nurse  works  a  hand-turned  sewing  machine, 
and  sings  to  it  as  she  works.  In  the  street  the  child 
sees  an  organ-grinder  singing  as  he  turns  his  handle : 
it  calls  '  mambro ' ;  the  nurse  catches  the  meaning  and 
the  child  is  overjoyed.  The  organ-grinder  has  a  mon- 
key: the  child  has  an  India-rubber  monkey  toy:  it  calls 
this  also  '  mambro.'  "  ^  The  individual's  vocabulary  is 
built  up  under  social  control  only  of  a  rough-and-ready 
sort.  It  is  adequate  for  general  purposes,  but  not  where 
accuracy  is  needed  or  where  slight  distinctions  are  very 
important.  Where  the  demands  are  more  exacting, 
vagueness  is  treacherous  and  leads  to  ambiguity. 

Abstract  Terms  particularly  subject  to  Vague- 
ness. Where  there  is  no  chance  to  appeal  to  perception 
as  a  test  for  the  meaning  of  a  term,  vagueness  is  almost 
certain  to  exist.  We  can  pick  up  the  word  just  as  the 
child  does,  but  it  is  another  thing  to  reproduce  the  idea. 
That  requires  mental  activity  of  a  high  degree.  The 
logician  stresses  the  fact  that  concepts  are  primary  and 
words  secondary.  What  is  meant  by  such  terms  as 
'  happiness,'  '  liberty,'  '  social  justice '  ?  I  who  have 
spent  years  in  analyzing  their  meanings  feel  that  I  have 
a  right  to  be  skeptical  of  some  glib  use  of  the  terms. 
"  When  we  come  to  words  of  which  the  logical  concept 
is  a  complex  relation,  an  obscure  or  intangible  attribute, 
the  defects  of  the  popular  conception  and  its  tendencies 
to  change  and  confusion  are  of  the  greatest  practical  im- 
portance. Take  such  words  as  '  Monarchy,'  '  tyranny,* 
^  Minto,  Logic,  Inductive  and  Deductive,  p.  83. 


48  THE  ESSENTIALS  OF  LOGIC 

*  civil  freedom,'  *  freedom  of  contract,'  'landlord,'  'gen- 
tleman,' 'prig,'  'culture,'  'education,'  'temperance,* 
'  generosity.'  Not  merely  should  we  find  it  difficult  to 
give  an  analytic  definition  of  such  words :  we  might 
be  unable  to  do  so,  and  yet  flatter  ourselves  that  we 
had  a  clear  understanding  of  their  meaning.  But  let 
two  men  begin  to  discuss  any  proposition  in  which 
any  such  word  is  involved  and  it  will  soon  be  found  that 
they  take  the  word  in  different  senses."  *  Such  terms 
are  really  technical  and  should  be  treated  as  such.  The 
difficulty  is,  however,  practical  as  well  as  scientific.  Peo- 
ple are  obliged  to  think  about  such  subjects  because 
of  their  duties  and  needs  as  citizens,  and  because  such 
terms  are  frequent  causes  of  dispute.  What  the  logician 
must  warn  against  is  dogmatism.  The  average  man  is 
not  easily  persuaded  that  familiarity  with  a  word  does 
not  involve  knowledge  of  what  it  means.  Such  dogmar 
tism  is  one  of  the  chief  causes  of  error. 

Logic  and  Language.  Logic  deals  with  thought, 
but  we  can  get  at  thought  only  through  language.  Now, 
language  is  not  a  transparent  medium ;  it  veils  as  well 
as  expresses  the  ideas  and  purposes  which  seek  utter- 
ance and  the  understanding  of  other  minds.  The  logi- 
cian must,  therefore,  be  equal  to  the  emergency  of  in- 
terpretation if  sufficient  clues  are  given.  "  The  practicing 
logician,  ever  seeking  behind  the  accidental  parlance 
the  necessary  sequence  of  idea,  studies  the  idiomatic  ex- 
pression of  thought,  with  which,  however,  and  not  with 
the  expression,  his  concern  truly  lies,"  * 

^  Minto,  Logic,  Inductive  and  Deductive,  p.  86. 
^  Macleane,  Reason,  Thought,  and  Language,  p.  9. 


THE  USE  AND  MISUSE  OF  LANGUAGE      49 

KEFERENCES 

Bode,  An  Outline  of  Logic,  chap.  ill. 
James,  Principles  of  Psychology,  vol.  ll,  chap.  xxn. 
Jones,  Logic,  Inductive  and  Deductive,  chap.  iv. 
Macleane,  Reason,  Thought,  and  Language,  Introduction. 
Minto,  Logic,  Inductive  and  Deductive,  part  n,  chap.  l. 
Stout,  Manual  of  Psychology,  bk.  rv,  chap.  V. 


CHAPTER  V 

CLASSIFICATION  AND  DIVISION 

Classification  and  Classes.  In  our  study  of  terms 
we  distinguished  class,  or  general,  terms  from  the  other 
kinds  of  terms.  It  is  our  present  purpose  to  study  in 
more  detail  the  nature  of  classes  and  the  character  of 
the  processes  by  which  they  are  obtained.  We  shall  see 
that  the  establishment  of  classes  involves  a  large  meas- 
ure of  mental  activity.  Certain  classes  suggest  them- 
selves quite  naturally,  while  others  are  formed  only  after 
a  deal  of  effort  has  been  expended  in  the  discovery  of 
hidden  relationships  between  things  apparently  different 
in  nature.  At  whatever  level  classes  are  formed,  com- 
parison, discrimination,  analysis,  and  construction  are 
at  work,  though  with  different  intensities.  It  must  never 
be  forgotten  that  an  object  is  not  a  member  of  a  class 
in  its  own  right,  but  because  a  class  has  been  conceived 
by  the  human  mind.  Man  and  nature  collaborate  in 
the  construction  of  classes.  When  a  class  has  been  es- 
tablished, however,  its  membership  is  potentially  deter- 
mined by  that  very  fact.  Having  conceived  of  verte- 
brates as  a  class,  we  cannot  refuse  membership  to  this 
or  that  creature  because  of  our  dislike  for  its  bad  habits 
or  its  ugly  appearance.  The  Gila  monster  is  as  good 
a  vertebrate  as  the  most  docile  pussy  that  ever  slept  in 
her  mistress's  lap. 

We  may  define  classification  as  the  process  of  group- 
ing things  together  according  to  their  possession  of  cer- 


CLASSIFICATION  AND  DIVISION  51 

tain  selected  common  attributes.  The  things  possessing 
these  attributes  are  the  members  of  the  class,  while  the 
class  is  the  members  taken  together.  Such  classes  may  be 
relatively  permanent  or  quite  temporary  and  occasional. 
The  following  quotation  will  illustrate  the  wide  range 
of  classes  which  the  logician  recognizes :  "  By  a  class 
will  here  be  meant  any  imagined  group  of  individual 
cases,  whether  real  or  unreal  —  a  group  in  which  every 
individual  is  supposed  to  resemble  all  the  others  in  some 
respects,  though  differing  in  others.  There  are  classes 
of  actions  and  events  just  as  of  everything  else ;  *  mir- 
acle '  is  a  class   name,  for  instance ;   or  '  coronation,' 

*  battle,'  '  eclipse  ' ;  in  fact  any  name  which  is  used  so 
as  to  admit  of  a  plural  —  either  simply,  as  '  miracles,' 

*  negroes,'  '  battles,'  or  in  the  more  circuitous  form  of 
'  pieces  of  gold,'  '  cases  of  deceit,'  and  so  on."  ^  There 
are  filmy  classes  as  well  as  the  more  ponderous  classes 
of  science.  Both  have  their  place  for  the  mind  of  the 
logician. 

The  Need  for  Classification.  The  world  man  is 
confronted  with  is  very  complex.  It  consists  of  objects 
and  events  of  every  conceivable  kind.  Moreover,  this  com- 
plex of  things,  actions,  and  events  does  not  come  ready- 
labeled.  The  world  is  not  like  a  museum  in  which  things 
of  a  kind  are  put  together  for  our  convenience.  Instead, 
they  are  scattered  about  in  space  and  time,  and  we 
must  be  ready  to  identify  them  wherever  they  are  found. 
But  identification  involves  mental  activity.  What  is  the 
character  of  this  mental  activity  and  why  is  it  aroused  ? 

The  simplest  form  of  identification  is  recognition. 
Psychologists  inform  us  that  recognition  is  often  imme- 
*  Sidgwick,  The  Use  of  Words  in  Reasoning,  p.  loO. 


52  THE  ESSENTIALS  OF  LOGIC 

diate,  that  an  object  arouses  associates,  and  these  give 
the  sense  of  familiarity.  "  Part  of  the  recognition  of  an 
object  that  is  not  handled  or  that  does  not  give  rise 
directly  to  movements  is  due  to  the  fact  that  its  uses 
are  appreciated,  that,  when  it  is  recognized,  one  knows 
at  once  what  to  do  with  it  and  how  to  use  it."  ^  Such 
immediate  recognition  is  an  unconscious  classification. 
The  character  of  the  object  is  appreciated  and  the 
proper  habits  and  attitude  are  aroused.  Thus  there  is  a 
practical  aspect  for  identification.  Similar  things  have 
similar  properties :  fire  burns ;  this  kind  of  tree  bears 
delicious  fruit ;  a  silent  baby  is  usually  in  mischief, 
etc.  If  we  had  to  deal  separately  with  each  thing, 
we  should  not  know  what  to  do  ;  it  would  be  impossible 
to  bring  past  experience  to  bear.  We  may  say,  then,  that 
classification,  unconscious  or  conscious,  is  the  only  way 
in  which  we  can  handle  our  complex  world  of  individual 
things. 

Types  of  Classification.  But  a  felt  identification 
is  not  sufficient  for  human  needs.  To  handle  things 
properly  and  commodiously  mankind  has  had  to  work 
out  methods  and  principles  of  grouping  adapted  to  the 
purpose  in  hand.  There  are  two  main  types  of  classifi- 
cation, the  artificial  and  the  natural,  and  these  corre- 
spond to  the  dominant  purpose.  In  an  artificial  classifi- 
cation, the  purpose  is  to  enable  us  to  handle  the  facts 
in  a  given  realm  as  quickly  and  easily  as  possible ;  that 
is,  the  purpose  is  practical.  In  a  natural  classification, 
the  purpose  is  to  allow  things  or  facts  to  arrange  them- 
selves in  accordance  with  their  essential  nature.  Let 
us  look  a  little  more  closely  at  these  two  types. 
^  Pillsbury,  Essentials  of  Psychology,  p.  209. 


CLASSIFICATION  AND  DIVISION  53 

Artificial  Classification.  In  artificial  classifications 
where  the  purpose  is  facility  in  handling,  some  obvious 
and,  as  a  rule,  external  attribute  is  selected  as  the  basis. 
A  good  example  of  this  type  is  the  method  by  which 
books  are  catalogued  in  a  library.  The  first  letter  of  the 
author's  name  determines  the  place  of  the  book  on  the 
shelves  and  in  the  catalogue.  If  this  simple  device  is 
insufficient,  the  subjects  are  likewise  arranged  alpha- 
betically. This  mode  of  artificial  classification  is  usually 
called  '  index  classification.' 

Another  kind  of  artificial  classification  is  the  so-called 
*  diagnostic  classification.'  The  purpose  at  work  here  is 
the  identification  of  an  object.  A  doctor  wishes  to  diag- 
nose a  disease  so  that  he  may  know  what  procedure  to 
adopt  in  his  treatment  of  it ;  or  a  collector  wishes  to 
label  a  butterfly  which  he  has  found.  In  both  cases  the 
the  search  is  made  for  characteristics  which  will  indi- 
cate the  group  to  which  the  object  belongs.  Nature- 
study  books  are  full  of  devices  for  identification  of  plants 
and  animals  according  to  pretty  obvious  traits. 

Natural  Classifications.  Natural  classifications  are, 
as  we  have  said,  based  upon  as  thorough  investigation 
of  the  nature  of  the  things  classified  as  is  attainable 
at  the  time.  The  purpose  is  to  find  some  arrangement 
which  corresponds  to  our  knowledge  and  reflects  a 
kinship  in  the  things  themselves.  Such  an  arrangement 
is  a  difficult  feat  to  achieve,  and  the  growth  of  science 
is  traceable  in  the  perfecting  of  systems  of  classi- 
fication. It  is  practically  always  necessary  to  pene- 
trate below  the  surface  and  to  build  on  those  underly- 
ing attributes  which  reveal  themselves  only  to  the  eye 
of   the  trained  observer.  "Thus  the  classification  of 


54  THE  ESSENTIALS  OF  LOGIC 

birds,  for  instance,  is  based  largely  upon  fundamental 
differences  in  anatomical  structure.  Birds,  not  as  we 
see  them,  but  as  they  are  when  stripped  of  plumage  and 
in  their  nakedness,  are  the  real  objects  of  consideration 
in  such  a  system  of  classification.  The  result  is  that  in 
the  same  group  there  will  appear  side  by  side  a  number 
of  birds  whose  surface  markings  are  exceedingly  dispar- 
ate, such  as  the  blue  jay  and  the  crow,  or  the  English 
sparrow  and  the  cardinal.  It  is  always  a  broadening 
experience,  as  regards  our  habits  of  thinking,  when  we 
are  able  to  discover  some  essential  similarity  at  the 
basis  of  a  marked  surface  dissimilarity."  ^ 

Natural  classification  is  scientific  classification  and 
reflects  all  the  purposes  and  methods  of  science.  The 
ultimate  aim  is,  of  course,  explanation,  but  there  is  also 
the  subordinate  aim  of  convenience.  This  combination 
of  purposes  is  very  well  brought  out  by  Jevons  :  "  By 
the  classification  of  any  series  of  objects  is  meant  the 
actual  or  ideal  arrangement  together  of  those  things 
which  are  like  and  the  separation  of  those  which  are  un- 
like, the  purpose  of  the  arrangement  being,  primarily, 
to  disclose  the  correlations  or  laws  of  union  of  properties 
and  circumstances,  and  secondarily,  to  facilitate  the  oper- 
ations of  the  mind  in  clearly  conceiving  and  retaining 
in  memory  the  characters  of  the  objects  in  question." 

Natural  Classification  in  the  Light  of  Evolu- 
tion. During  the  eighteenth  and  the  first  half  of  the  nine- 
teenth century,  scientists  believed  in  the  existence  of 
natural  kinds  of  species  which  were  changeless  in  char- 
acter and  sharply  distinct  from  one  another.  The  task 
of  the  anatomist  was  to  dissect  these  species  and  deter- 
^  Hibben,  Logic,  Deductive  and  Inductive,  p.  58. 


CLASSIFICATION  AND  DIVISION  55 

mine  their  essential  or  defining  marks.  The  hope  was 
to  enumerate  and  describe  these  fixed  species  once  for 
all,  and  then  to  erect  a  scheme  of  classification  into 
which  they  would  all  fit.  But  continued  investiga- 
tion convinced  naturalists  that  there  was  something 
scholastic  and  unreal  in  sharp  distinctions ;  that  spe- 
cies merged  with  one  another  on  the  edges.  With 
the  gradual  rise  of  the  theory  of  evolution  it  came  to 
be  recognized  that  there  are  genetic  relationships  run- 
ning all  through  the  organic  realm  and  that  species  are, 
so  to  speak,  abstractions  which  over-simplify  nature. 
Species  are  not  immutable,  but,  instead,  shade  over  into 
one  another.  Classification  is  a  tool  which  must  not  be 
read  into  the  complex  realm  of  things  too  naively. 

Character  of  Systematic  Classification.  Partic- 
ular classes  are  formed  by  grouping  objects  together 
according  to  their  likenesses  and  differences.  But  a 
further  task  ensues,  that  of  showing  the  relations  be- 
tween the  classes  thus  formed.  We  are  not  satisfied  to 
leave  particular  classes  in  isolation,  but  demand  a  sys- 
tem of  classification  in  which  classes  are  arranged  in 
accordance  with  conceived  relations  of  cobrdination.h 
subordination^  and  superordination.  Such  systems 
must  express  an  internal  unity  which  is  manifested  in 
various  ways  in  the  subordinate  classes.  All  the  classes 
must  have  certain  attributes  in  common,  and  these  com- 
mon attributes  must  not  contradict  the  more  specific 
attributes  which  differentiate  the  subordinate  classes 
from  one  another.  To  put  the  matter  less  technically : 
classification  works  within  some  field  of  objects  and 
seeks  to  arrange  them  by  selecting,  first,  those  attri- 
butes which  they  all  possess,  and,  secondly,  those  groups 


56 


THE  ESSENTIALS  OF  LOGIC 


of  further  and  more  specific  attributes  which  divide  the 
whole  field  into  related  yet  distinct  classes.  So  far  as 
possible  the  differences  which  divide  the  whole  into 
parts  must  be  seen  in  their  relation  to  the  fundamental 
similarities.  A  particular  class  is  a  species  (difference) 
of  (similarity)  the  genus.  A  good  classification  should 
make  it  possible  to  see  any  fact  in  the  light  of  the 
whole.  The  following  example  brings  out  this  presence 
of  an  underlying  agreement  manifesting  itself  in  differ- 
ent ways:^ — 

Vegetable  Kingdom 


Rootless,  leaf- 
less,  stemless 

plants 
{Thallophytd) 


Moss-like 

plants 
(Bryophyta) 


Fern-like 

plants 
(PteridopTiytd) 


Seed-bearing 

plants 
(Spermaphyta) 


f^ 


OB  ^ 


§2. 


;2^ 


wis  V 


ca   Si 


f1 


to    C    g< 


tJ 

-S 


w 


The  student  should  examine  the  type  of  classifica- 
tion found  in  any  good  textbook  in  biology  in  order  to 
familiarize  himself  with  the  mechanism  of  the  process. 

Classification  and  Division.  There  is  a  very  close 
connection  between  classification  and  another  logical 
process  called  *  division.*  The  main  difference  in  the 
meaning  of  the  two  terms  is  this :  that  when  we  classify, 
we  think  of  ourselves  as  moving  upward  from  the  indi- 

*  Quoted  from  Tajlor,  Elementary  Logic,  p.  45. 


CLASSIFICATION  AND  DIVISION  57 

vidual  things  to  schemes  of  arrangement  according  to 
likeness  and  difference ;  that  when  we  divide,  we  think 
of  ourselves  as  moving  downward  from  the  more  gen- 
eral and  inclusive  modes  of  grouping  to  more  specific 
sub-classes.  Such  a  distinction  is,  however,  rather  arti- 
ficial, for,  in  the  solution  of  any  real  problem  of  ar- 
rangement, our  thought  moves  in  both  directions  at 
once.  Yet,  while  recognizing  to  the  full  this  double 
movement  of  thought,  it  still  remains  true  that  logical 
division  is  a  method  with  a  definitely  conceived  form 
which  can  be  used  as  a  test  of  any  classification.  As  a 
method,  it  is  inclined  to  be  more  doctrinaire  and  a 
priori  than  classification. 

Technical  Terms  used  in  Division.  Division  is  a 
process  which  may  be  carried  through  many  stages. 
The  general  class  with  which  it  starts  is  called  the 

♦  summum  genus,'  that  is,  the  highest  genus.  The  sub- 
class with  which  it  stops  is  called  the  '  infimas  species,' 
that  is,  the  lowest  species.  Between  these  two  extremes, 
the  terms  *  species '  and  '  genus '  are  used  as  purely 
relative  terms.  In  any  series,  the  class  above  is  the 
genus  of  the  class  below  which  is  its  species.  The  class 
directly  above  is  the  '  proximum  genus '  of  the  species 
just  below.  Where  more  than  one  species  have  the 
same  proximum  genus  they  are  called  '  coordinate  spe- 
cies.'   The  coordinate  species  of  a  genus  are  called  its 

*  constituent  species.'  The  principle  used  in  dividing 
is  called  the  '  fundamentum  divisionis,'  or  basis  of  di- 
vision. It  is  that  aspect  of  the  summum  genus  which 
enables  us  to  separate  its  constituent  species.  The  dif- 
ferentia of  a  species  is  that  characteristic  which  distin- 
guishes it  from  its  coordinate  species. 


68  THE  ESSENTIALS  OF  LOGIC 

Rules  of  Division.  To  be  valid,  a  logical  division 
must  observe  the  following  rules  :  — 

1.  A  division  must  be  complete.  A  complete  division 
is  one  which  exhausts  the  constituent  species  of  the 
main  class. 

The  necessity  for  this  rule  is  at  once  apparent.  The 
neglect  of  any  species  may  easily  lead  to  confusion  in 
both  theory  and  practice. 

2.  The  constituent  species  into  which  the  genus  is 
divided  must  not  overlap.  A  division  is  imperfect  if  an 
individual  may  belong  to  two  species  at  the  same  time. 

A  few  words  in  regard  to  these  rules  may  be  advisa- 
ble. An  incomplete  division  may  be  due  to  ignorance, 
lack  of  persistence,  or  to  the  special  difficulties  of  the 
field.  When  the  last  is  the  case,  it  is  sometimes  met  by 
forming  a  miscellaneous  class  to  include  obscure  data. 
Such  a  miscellaneous  class  points  to  the  tentative  char- 
acter of  the  classification  which  the  division  reflects.  A 
violation  of  the  second  rule  leads  to  cross-division  and 
is  the  consequence  of  the  employment  of  more  than  one 
basis  of  division.  The  division  of  the  citizens  of  a  coun- 
try into  the  rich,  the  poor,  and  the  educated  is  an  ex- 
ample of  cross-division. 

Forms  of  Division.  There  are  two  forms  of  di- 
vision, dichotomous  and  classificatory  division.  These 
are  readily  distinguishable.  In  dichotomous,  or  bifur- 
cate, division  the  genus  is  cut  into  two  classes,  those 
which  possess  the  character  and  those  which  do  not. 
The  one  is  a  positive  group,  the  other  is  an  indefinite, 
negative  group.  Together,  however,  they  are  exhaus- 
tive of  the  genus.  This  process  can  be  further  continued 
on  either  of  the  two  groups.  The  other  form  of  division. 


CLASSIFICATION  AND  DIVISION  59 

wliieh  I  have  called  '  classificatory,'  is  the  reverse  aspect 
of  any  system  of  classification.  The  species  into  which  the 
genus  divides  are  positive  and  coordinate ;  their  num- 
ber is  determined  by  the  nature  of  the  field.  We  may 
speak  of  such  division  as  '  analytic '  and  of  the  corre- 
sponding classification  as  '  synthetic' 

Dichotomous  Division.  While  dichotomous  divi- 
sion is  simple  and  exhaustive,  it  easily  becomes  unwieldy 
when  carried  far.  Moreover,  one  side  is  negative  and 
indefinite.  All  that  is  known  about  it  is  that  it  lacks 
the  positive  character  the  other  side  possesses.  Under 
certain  circumstances,  however,  the  lack  of  a  quality 
may  be  as  interesting  as  its  possession.  Thus  the  di- 
vision of  the  population  into  voters  and  non-voters,  or 
of  the  working-classes  into  skilled  and  unskilled,  gives 
us  two  groups  which  are  really  coordinate.  Where  we 
are  interested  in  some  part  of  the  field  rather  than  in 
the  whole,  tracing  by  dichotomy  may  be  the  easiest 
way.  The  following  example,  usually  called  the  '  Tree 
of  Porphyry,'  makes  the  method  clear :  — 

Substance 


Corporeal  Incorporeal 


Animate  Inanimate 


Sensible  Insensible 


Rational  Irrational 


Mortal  Immortal 

This  method  of  division  may  be  made  instrumental 
to  the  working-out  of  a  definition  of  a  term.  Thus,  ac- 
cepting the  adequacy  of  the  above  tree^  we  can  define 
man  as  'a  corporeal  substance,  animate,  sensible,  ra- 
tional,  and  mortal.'    Another  example   will  serve  to 


60  THE  ESSENTIALS  OF  LOGIC 

bring  out  this  use  sufficiently.  "  The  term  to  be  defined 
is  '  tuber ' ;  the  genus  to  which  it  is  to  be  referred  is 
*  stem.' 

Stem 


creeping      not  creeping 


underground         not  underground 


much  thickened        not  much  thickened 


possessing  leaf-buds  not  possessing  leaf-buds 

in  the  form  of  '  eyes  *  in  the  form  of  '  eyes ' 

"  In  this  division,  we  reach,  as  our  definition  of  a 
tuber,  'a  stem  creeping  underground,  much  thickened, 
and  possessing  leaf-buds  in  the  form  of  eyes.' "  ^ 

ClassifLcatory  Division.  This  form  of  division  is, 
in  its  final  expression,  the  same  as  a  system  of  classifica- 
tion. The  species  under  any  genus  must  be  coordinate 
and  exhaustive.  It  should  be  remembered  that  the  move- 
ment in  division  is  downward  from  the  general  to  the 
more  particular,  while  in  classification  it  is  upward  from 
the  particulars  to  the  more  general.  Only  one  other 
point  needs,  I  think,  to  be  mentioned.  The  funda- 
mentum  divisionis  which  is  selected  depends  partly 
upon  the  purpose,  partly  upon  the  character  of  the 
subject-matter. 

Dangers  to  be  guarded  against.  Imperfect  classi- 
fication and  division  lead  to  the  identification  of  things 
and  ideas  which  should  be  discriminated.  This  is,  as  we 
have  seen,  the  chief  cause  of  ambiguity.  It  is,  in  fact, 
impossible  to  treat  definition  and  ambiguity  apart  from 
the  consideration  of  classification  and  division,  for  in 
these  processes  we  are  studying  the  methods  by  which 
^  Joseph,  An  Introduction  to  Logic,  p.  113. 


CLASSIFICATION  AND  DIVISION  61 

the  mind  orders  and  arranges  its  material.  For  the  ma- 
jority, an  examination  of  the  systems  established  in  the 
various  sciences  is  of  less  value  than  the  critical  analy- 
sis of  less  formal  and  better-known  subjects.  The  chief 
danger  to  be  guarded  against  is  the  merging  together 
of  things  which  should  be  distinguished.  Natural  law 
should  not  be  confused  with  moral  law,  nor  this  with 
statute  law.  Education  should  not  be  identified  with 
erudition,  nor  cleverness  with  talent.  'Democracy' 
should  not  be  used  as  a  blanket-term  to  cover  repre- 
sentative institutions  and  the  absence  of  caste.  The 
proper  use  of  terms  is  the  result  of  the  critical  discrimi- 
nation of  different  meanings,  and  these  meanings  them- 
selves rest  upon  the  keen  perception  and  exhaustive 
treatment  of  likenesses  and  differences.  After  classifica- 
tion comes  definition  which  is  its  fruition. 

REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  v. 
Hibben,  Logic,  Deductive  and  Inductive,  chap.  VI. 
Jones,  Logic,  Inductive  and  Deductive,  chap.  ni. 
Joseph,  An  Introduction  to  Logic,  chap.  v. 
Minto,  Logic,  Inductive  and  Deductive,  part  ll,  chap.  I. 
Schiller,  Formal  Logic,  chap.  Vl. 


CHAPTER  VI 

PRINCIPLES  OF  DEFINITION 

Why  Definition  is  Needed.  In  a  former  chapter 
we  saw  why  language  is  a  necessary  instrument  of 
thought  and  what  some  of  its  imperfections  are.  "The 
logical  ideal  of  the  relation  between  words  and  thoughts 
is,  of  course,  that  every  thought  should  have  its  own 
name,  and  every  name  should  have  its  own  meaning."  ^ 
This  ideal  is  unrealizable  because  language  is  always 
changing.  New  shades  of  meaning  are  constantly  being 
developed  and  old  distinctions  falling  into  disuse.  But 
ignorance  and  mental  indolence  are  also  at  work  to  make 
the  use  of  words  unclear.  The  correct  employment  of 
words  depends  upon  three  things:  a  large^ vocabulary, 
a  fund  of  clear  meanings,  and  the  proper  adjustment 
of  the  two.  Unless  these  three  things  are  forthcom- 
ing, there  will  be  confusion  in  the  individual's  mind 
and  misunderstanding  when  he  attempts  to  communi- 
cate his  ideas.  Probably  John  Locke  has  pointed  out 
these  dangers,  which  only  definition  can  correct,  as  well 
as  any  one :  — 

"  For  he  that  shall  well  consider  the  errors  and  ob- 
scurity, the  mistakes  and  confusion,  that  are  spread  in 
the  world  by  an  ill  use  of  words,  will  find  some  reason 
to  doubt  whether  language,  as  it  has  been  employed,  has 
contributed  more  to  the  improvement  or  hindrance  of 
knowledge  amongst  mankind.  How  many  are  there,  that, 
*  Davidson,  The  Logic  of  D^nition,  p.  2. 


PRINCIPLES  OF  DEFINITION  63 

when  they  would  think  on  things,  fix  their  thoughts 
only  on  words,  especially  when  they  would  apply  their 
minds  to  moral  matters ;  and  who,  then,  can  wonder  if 
the  result  of  such  contemplations  and  reasonings  about 
little  more  than  sounds,  whilst  the  ideas  they  annex  to 
them  are  very  confused  and  very  unsteady,  or  perhaps 
none  at  all ;  who  can  wonder,  I  say,  that  such  thoughts 
and  reasonings  end  in  nothing  but  obscurity  and  mis- 
take, without  any  clear  judgment  or  knowledge  ?  "  * 

We  have  said  that  definition  can  be  of  great  assist- 
ance in  overcoming  such  confusion  and  misunderstand- 
ing. But  definition  is  a  process  which  works  with  words 
and  ideas.  The  individual  must  be  capable  of  handling 
thousands  of  concepts  and  of  distinguishing  nice  shades 
of  meaning ;  he  must  also  have  a  fairly  large  fund  of 
knowledge.  On  the  verbal  side,  he  must  be  able  to  dis- 
criminate the  uses  of  words.  These  are  really  two  as- 
pects of  the  same  process,  for  I  very  much  doubt  whether 
the  Mrs.  Malaprops  are  much  more  sensible  in  their  use 
of  ideas  than  in  their  use  of  words.  No  one  can  make 
nice  discriminations  between  words  who  cannot  do  the 
same  for  ideas.  Both  acts  are  achievements  which  do 
not  come  without  effort  and  the  establishment  of  good 
mental  habits.  And  it  is  the  belief  of  the  logician  that 
the  study  of  logic  should  assist  in  the  formation  of  such 
habits.  It  stresses  the  need  and  gives  the  general  rules 
and  methods  which  should  be  followed. 

The  Purpose  and  Nature  of  Definition.  Defini- 
tion has  a  double  aspect.  On  the  one  hand,  terms  are 
defined  in  order  to  test  correspondence  in  the  use  of 


words.  Two  disputants  wish  to  discover,  for  example, 

*  Essay  concerning  Human  Understanding,  l>k.  lii,  chap.  XI. 


64  THE  ESSENTIALS  OF  LOGIC 

whether  they  have  the  same  understanding  for  a  pivotal 
word.  If  they  do  have,  they  can  profitably  proceed  iu 
their  discussion ;  if  they  do  not  have  the  same  idea,  they 
must  go  further  back  until  they  find  some  common 
gi'ound  of  agreement.  On  the  other  hand,  definition 
arises  as  the  tempqraryjcompletion  of  a  field  of  investi- 
gation. A  definition  is  a  summary  in  which  ideas  "are 
ordered  in  relation  to  one  another.  A  definition  is  a 
product  just  as  the  meanings  concerned  are  products. 
Looked  at  in  this  genetic  way,  definitions  are  seen  to 
be  tentative. 

There  are  two  aspects  to  every  definition  because  both 
ideas  and  words  are  involved.  Ideas  must  be  achieved 
and  analyzed,  and  the  meaning  obtained  must  be  at- 
tached to  a  word  as  its  meaning.  According  to  the  set- 
ting, either  of  these  aspects  may  be  emphasized  more 
than  the  other.  Logic  has  recognized  this  possibility  in 
the  distinction  between  real  and  verbal  definitions. 
When  the  purpose  is,  predominantly,  to  indicate  how 
we  intend  to  use  a  term,  the  result  is  a  verbal  definition. 
Dictionary  definitions  are  of  assistance  here  because 
they  offer  the  average  or  common  meaning.  It  must  be 
remembered  that  the  peculiar  purpose  or  point  of  view 
of  the  individual  enters  in  to  qualify  the  average  mean- 
ing, which  is  in  many  ways  an  abstraction.  Verbal  defi- 
nitions represent  past  achievements.  When,  on  the  other 
hand,  we  are  interested  primarily  in  getting  an  ade- 
quate idea,  we  are  said  to  achieve  real  definitions.  We 
try  to  get  behind  words  to  the  things  and  concepts  for 
which  they  stand. 

To  define  is,  then,  to  indicate  the  meaning  of  a  word 
by  achieving  an  analyzea^ncept.  Definition  is  an  at- 


PRINCIPLES  OF  DEFINITION  65 

tempt  to  attain  to  a  definite  meaning.  On  the  mental 
side,  it  is  largely  an  outgrowth  of  classification  and 
division. 

Logic  stresses  General  Terms.  Logic  has  been  so 
impressed  by  scientific  method  that  it  has  connected 
definition  with  classification  and  division.  It  is  for  this 
reason  that  writers  in  logic  usually  define  definition  as 
the  process  of  determining  the  connotation  of  a  term. 
It  will  be  remembered  that  general  or  class  terms  have 
two  aspects,  the  things  to  which  they  apply  and  the  at- 
tributes wliich  they  imply.  To  define  such  a  term  is  to 
state  the  attributes  characteristic  of  the  class  and,  indi- 
rectly, to  establish  its  denotation. 

It  is  because  vague  terms  become  ambiguous  that  the 
need  for  definition  is  felt.  We  wish  to  know  exactly 
what  a  term  stands  for.  For  example,  is  a  '  communist ' 
the  same  as  a  '  communard' ?  Now,  in  the  case  of  proper 
names  the  ambiguity  can  be  overcome  by  pointing  to 
the  person  meant  or  by  adding  descriptive  words  to 
make  the  reference  definite.  Much  the  same  process  is 
necessary  for  abstract  terms  which  are  simple.  If  a  man 
asks  me  what  'redness'  means,  I  can  only  reply  by  call- 
ing his  attention  to  some  red  object  and  indicating  the 
quality.  I  must  assume  his  ability  to  abstract  the  qual- 
ity and  make  it  an  object  of  thought.  But  the  applica- 
tion of  class  terms  cannot  be  indicated  in  this  simple 
fashion.  It  is  true  that  I  can  illustrate  the  use  of  such 
a  term  by  an  example  or  specimen.  "  But  any  example 
might  illustrate  a  variety  of  things ;  if  two  persons,  each 
of  whom  was  entirely  imacquainted  with  the  language 
of  the  other,  should  try  to  communicate  by  pointing  to 
objects  to  indicate  the  meaning  of  the  words  they  were 


66  THE  ESSENTIALS  OF  LOGIC 

using,  they  would  illustrate  the  uncertainly  of  this  method 
in  its  extreme  form.  If  one  of  them  should  point  to  a 
horse,  he  might  mean  any  one  of  a  dozen  different 
things :  horse,  or  simply  animal,  or  useful  animal,  or 
large  object,  or  gray,  or  beautiful,  or  dangerous,  and  so 
on.    '■ 

Definition  and  Classification.  It  can  readily  be 
seen  that  real  definition,  or  the  process  of  securing 
clearer  and  more  adequate  ideas,  is  bound  up  with  the 
logic  of  classification.  To  obtain  a  clear  idea  of  a  class 
we  must  see  it  as  a  part  of  a  system.  Thus  the  defini- 
tion of  a  triangle,  '  as  that  section  of  a  cone  which  is 
formed  by  a  plane  passing  through  the  vortex  perpen- 
dicularly to  the  base,'  reveals  the  triangle  as  related  to 
a  system  of  geometrical  objects.  The  more  scientific  a 
definition,  the  more  it  is  the  reflection  of  a  classified 
field.  Definition  is  possible  only  when  there  is  organized 
knowledge.  In  a  very  true  sense,  the  whole  of  logic 
concerns  itself  with  the  method  of  obtaining  well-defined 
ideas. 

The  Verification  of  Meaning.  The  verification  of 
the  meaning  of  a  term  is  partly  a  social  process,  partly 
a  process  of  investigation  of  the  things,  actions,  or 
events  indicated  by  the  term.  There  is  always  a  rough 
approximation  of  the  meaning  with  which  to  begin. 
The  problem  is  to  narrow  down  and  define  the  use. 
Take,  for  example,  such  words  as  '  freedom,'  '  liberty,' 
*  justice,'  and  '  equality.'  These  words  are  often  on 
people's  lips,  yet  they  are  used  vaguely.  They  refer  to 
the  same  social  field,  but  stress  different  aspects  of  that 
field.  They  are  allied  while  at  the  same  time  distinct. 
^  Jones,  Logic,  Inductive  and  Deductive,  p.  58. 


PRINCIPLES  OF  DEFINITION  67 

What  must  be  done  in  order  to  verify  their  proper 
meanings  ? 

There  are  two  levels  in  the  verification  of  meaning. 
The  first  is  to  determine  how  the  word  is  actually  used ; 
the  second  is  to  advance  to  a  scientific  concept  which 
fits  into  a  thoroughly  classified  and  analyzed  depart- 
ment of  investigation.  The  first  level  gives  us  a  clear 
popular  concept ;  the  second,  if  successful,  gives  us  a 
scientific  concept.  It  goes  without  saying,  however,  that 
the  scientific  concept  is  essentially  a  summary  of  the 
total  field  under  investigation.  It  is  difficult,  if  not  im- 
possible, to  get  a  clear  vision  of  its  contents  and  impli- 
cations apart  from  an  intimate  acquaintance  with  the 
field.  Let  the  reader  pick  up  a  book  on  a  subject  with 
which  he  is  not  familiar  and  attempt  to  understand  the 
technical  terms  while  neglecting  the  facts  and  argument 
with  which  they  are  connected,  and  he  will  understand 
that  the  verification  of  scientific  concepts  is  one  with 
scientific  investigation  itself. 

But  logic  is  also  concerned  with  a  more  general  play 
of  the  mind  which  works  for  clear  meanings  whether 
at  the  level  of  common  sense  or  at  that  of  science.  It 
can  never  be  amiss  to  run  over  the  denotation  of  a  term 
and  to  discuss  with  others  their  understanding  of  its 
exact  shade  of  meaning.  The  more  complex  the  field, 
the  more  valuable  is  this  practice.  This  method  of  veri- 
fication goes  back  to  the  Greeks,  who  made  much  use 
of  it  when  they  realized  how  uncertainly  terms  are  em- 
ployed by  the  majority  of  men.  Socrates  crystallized 
this  procedure  and  it  has  consequently  been  called  '  So- 
cratic  induction  '  and  '  Socratic  dialectic '  according  as 
stress  is  laid  upon  the  running  over  of  examples  or 


68  THE  ESSENTIALS  OF  LOGIC 

upon  the  value  of  free  discussion  by  means  of  question 
and  answer.  Every  one  should  read  some  one  at  least 
of  the  earlier  Socratic  dialogues  of  Plato  in  which  this 
suggestive  method  is  used  as  a  tool  for  deepening  and 
defining  the  meanings  of  common  terms.  When  this 
method  is  skillfully  applied,  one  can  see,  as  it  were, 
meanings  grow  under  one's  eyes.  Under  such  condi- 
tions, the  definition  becomes  a  living  thing  into  whose 
secrets  one  is  admitted.  "  The  truth  is  —  as  most  read- 
ers of  Plato  know,  only  it  is  a  truth  difficult  to  retain 
and  apply  —  that  what  we  gain  by  discussing  a  defini- 
tion is  often  but  slightly  represented  in  the  superior 
fitness  of  the  formula  that  we  ultimately  adopt ;  it  con- 
sists chiefly  in  the  greater  clearness  and  fullness  in 
which  the  characteristics  of  the  matter  to  which  the 
formula  refers  have  been  brought  before  the  mind  in 
the  process  of  seeking  for  it.  .  .  .  In  comparing  differ- 
ent definitions  our  aim  should  be  far  less  to  decide 
what  we  ought  to  adopt,  than  to  apprehend  and  duly 
consider  the  grounds  on  which  each  has  commended  it- 
self to  reflective  minds.  We  shall  generally  find  that 
each  writer  has  noted  some  relation,  some  resemblance 
or  difference,  which  others  have  overlooked ;  and  we 
shall  gain  in  completeness,  and  often  in  precision,  of 
view  by  following  him  in  his  observations,  whether  or 
not  we  follow  him  in  his  conclusions."  ^  This  method  is 
especially  advisable  in  the  social  sciences  or  in  the 
handling  of  those  general  topics  which  arise  so  fre- 
quently for  discussion.  How  few  of  us  know  exactly 
what  we  mean  by  such  terms  as  'nature,'  'justice,' 

^  Sidgwick,  Political  Economy,  pp.  52-53  ;  quoted  from  Minto,  Logic, 
Ifiductive  and  Deductive,  p.  90. 


PRINCIPLES  OF  DEFINITION  69 

*  law,' '  beauty,'  etc. !  Familiarity  with  the  word  deceives 
us  into  the  belief  that  we  understand  the  concept  of 
which  it  is  the  sign. 

Rules  of  Defijiition.  The  following  rules  of  defini- 
tion should  put  the  student  on  guard  against  bad  defi- 
nitions and  should  give  him  some  assistance  in  his 
attempts  to  formulate  good  definitions.  All  the  techni- 
cal terms  needed  have  already  been  given  in  the  chap- 
ter on  "  Division  and  Classification." 

1.  A  good  definition  is  hy  proximate  genus  and  \ 
essential  difference.  We  should  try  to  find  a  larger  | 
class  with  which  to  connect  the  thing  defined  and  then  ' 
analyze   and  state  the  features  of   the  thing  defined 
which  distinguish  it  from  the  other  members  of  this 
larger  class.  By  relating  it  to  this  larger  class,  we  in  a 
measure  explain  it,  for  we  connect  it  with  something 
more  familip-r.  We  are  then  in  a  position  to  pass  down  to 
important  differences.  This  rule  of  definition  brings  out 
its  intimate  connection  with  classification  and  division. 

When  the  difference  offered  is  not  essential  or  is 
vaguely  conceived,  we  have  an  imperfect  definition.  Many 
imperfect  definitions  are  suggestive  because  they  reveal 
the  fact  that  the  topic  concerned  has  not  yet  been 
clearly  analyzed  and  classified. 

2.  A  term  should  not  he  defined  hy  means  of  itself  j 
or  of  words  which  are  synonymous  with  it.  We  should  • 
avoid  tautology.  Dictionaries  transgress  against  this 
obvious  rule  only  too  frequently.  It  is  hardly  enlight- 
ening to  be  told  that  life  is  a  '  vital  force,'  or  that  pleas- 
ure is  '  agreeable  sensation,'  or  that  altruistically  is  '  in 
an  altruistic  manner.'  ^  More  serious  cases  of  defining 

'  For  other  examples  see  Davidson,  The  Logic  of  Definition,  p.  62. 


70  THE  ESSENTIALS  OF  LOGIC 

a  thing  by  itself  are  the  following :  '  Life  is  that  which 
distinguishes  living  from  non-living  things,'  *A  cause 
is  the  invariable  and  unconditional  antecedent  of  a 
phenomenon.'  Relative  terms  are  often  defined  in  terms 
of  each  other.  The  consequence  is  that  we  go  from  one 
to  the  other  and  then  back  again  and  are  not  greatly 
advanced  by  the  process. 

3.  A  definition  should  he  neither  too  hroad  nor  too 
narrow.  It  should  not  cover  a  larger  field  than  usage 
warrants  nor  a  narrower  field.  Thus,  to  define  a  square 
*  as  a  rectangle,'  or  a  root  as  '  that  part  of  a  plant  which 
grows  underground,'  would  be  cases  of  overbroad  defi- 
nitions ;  while  to  define  a  dog  *  as  a  domesticated  ani- 
mal used  to  guard  the  home '  would  obviously  be  too 
narrow.  This  rule  is  really  only  a  development  of  the 
first  rule,  for,  had  the  genus  and  essential  difference 
been  worked  out,  the  resultant  definition  j^rould  have 
been  neither  too  broad  nor  too  narrow. 

4.  A  definition  should  not  he  expressed  in  ohscure 
or  figurative  language.  The  purpose  of  a  definition 
should  be  kept  clearly  in  mind.  Where  the  field  is 
necessarily  technical,  the  use  of  technical  terms  is  in- 
evitable, and  these  must  not  be  considered  obscure 
however  little  they  are  understood  by  the  layman.  "  The 
scientific  definition  of  life  as  the  dynamic  condition  of 
an  organism  would  not  be  that  of  the  plain  man.  The 
plain  man  thinks  he  knows  what  ivy  is,  and  is  not 
much  wiser  for  being  told  that  it  is  an  epiphytic  plant 
of  the  genus  hedera.  But  he,  too,  may  learn  something 
from  the  definition  of  sickness  as  Nature's  protest 
against  the  misdirection  of  her  forces,  or  from  St.  Aus- 
tin's phrase,  '  virtus  est  ordo  amoris '  —  the  orderly  and 


PRINCIPLES  OF  DEFINITION  71 

progressive  unfolding  of  love."^  In  this  connection,  Dr. 
Johnson's  famous  definition  of  network,  as  "  anything 
reticulated  or  decussated  at  equal  distances  with  inter- 
stices between  the  intersections,"  is  usually  given  as  a 
horrible  example  of  misapplied  learning. 

6.  A  definition  should  he  expressed  in  positive  terms  /^ 
whenever  possible.  A  definition  should  tell  what  a  1/ 
thing  is,  rather  than  what  it  is  not.  But  ultimate  con- 
ceptions can  often  be  suggested  and  indicated  by  neg- 
ative terras.  Thus,  a  geometer  may  define  a  point  as 
that  which  has  neither  length,  breadth,  nor  thickness. 
We  must,  however,  stress  the  meaning  of  a  definition 
instead  of  its  form.  Where  the  concept  defined  is,  itself, 
essentially  negative,  there  must  be  a  negative  element 
in  the  definition.  *  Liberty  is  absence  of  restraint.' 
*  Uncertainty  is  the  want  of  a  fixed  mental  attitude.* 
'A  bachelor  is  an  unmarried  man.'  'Injustice  is  the 
not  keeping  of  covenant.'  These  are  all  negative  in 
form,  but  as  positive  as  their  contents  permit. 

Other  Forms  of  Definition.  We  have  stressed 
what  may  be  called  the  ideal  form  of  definition,  that 
through  genus  and  diflPerentia.  In  the  Latin  terminol- 
ogy of  logic  it  is  called  definition  per  proximum  genus 
et  differentiam  vel  differentias.  It  is,  as  we  have  con- 
stantly pointed  out,  the  reflection  of  a  system  of  clas- 
sification. When  such  a  basis  cannot  be  appealed  to, 
resort  must  be  had  to  other  methods  of  making  the 
meaning  of  a  term  clear.  The  methods  usually  adopted 
in  such  cases  are  as  follows :  — 

1.  Description.  Individual  things  or  events  can  be  1 
described  in  such  a  way  as  to  make  the  application  of 

^  Macleane,  Reason,  Thought,  and  Language,  p.  175. 


72  THE  ESSENTIALS  OF  LOGIC 

the  term  clear.  It  is  possible  to  select  outstanding  prop- 
erties or  traits  which  serve  to  distinguish  one  thing 
from  another.  Accurate  word-painting  is  an  art  which 
can  be  used  to  reproduce  in  the  mind  of  the  hearer  or 
reader  the  essential  characteristics  of  the  scene  or  per- 
son described. 
I  2.  Examples.  If  weU-selected  examples  of  the  term 
'  under  discussion  are  given,  it  is  possible  to  get  a  pop- 
ular concept,  at  least,  of  the  term.  What  does  '  good  * 
mean  ?  How  natural  it  is  to  run  over  examples  of  good 
men !  In  doing  so,  we  are  trying  to  pass  from  the  de- 
notation to  connotation,  a  part  of  the  denotation  being 
less  doubtful  than  the  exact  marks  which  make  a  man 
good.  It  depends  upon  the  purpose  how  far  the  use  of 
example  is  satisfactory.  If  this  be  practical,  examples 
may  meet  the  need  and  thus  serve  as  a  sort  of  defini- 
tion. 
I  3.  Genetic  formula.  It  is  frequently  important  to 
I  know  how  a  thing  is  made.  Chemical  formulae  do  not 
tell  us  the  essential  properties  of  the  thing  unless  they 
reveal  to  us  a  scheme  of  classification  connected  with 
such  properties.  They  are,  however,  of  distinct  utility. 
Recipes,  diagrams,  instructions  are  practical  definitions 
of  a  genetic  kind. 

The  need  lying  back  of  definition  is  to  understand 
the  application  of  a  term.  Whatever  meets  this  need 
is,  in  the  broadest  sense  of  that  term,  a  definition. 
Hence  the  logician  must  not  be  dogmatic  and  set  up 
only  one  type  of  definition.  Purpose  and  setting  must 
♦  be  taken  into  account.  "  In  defining  we  look  to  what 
appears  to  be,  for  our  immediate  purpose,  some  striking 
feature.    We  try  to  define   everything  by  something 


PRINCIPLES  OF  DEFINITION  73 

better  known.  A  fox  would  not  be  defined  in  the  same 
way  by  a  huntsman  and  by  a  naturalist.  Death,  which 
to  the  physician  is  the  cessation  of  all  vital  functions, 
is  to  the  singer  of  Hawthornden  '  the  thaw  of  all  those 
vanities  which  the  frost  of  life  holdeth  together.'  "  ^ 

The  Fredicables.  Logic  is  a  very  old  science  and 
has  accumulated  traditions  and  technical  names.  It  is 
hardly  justifiable  to  neglect  these  inherited  distinctions, 
yet  they  must  not  be  allowed  to  occupy  too  much  space. 
Typical  of  this  logical  tradition  are  the  '  Five  Fredi- 
cables.' A  predicable  is  literally  that  which  can  be 
predicated.  Now,  only  that  which  is  a  general  term  can 
be  predicated  of  a  subject.  I  can  say  that  this  object 
is  a  cat,  but  I  can't  assert  of  any  other  object  that  it 
is  this  particular  object  which  I  have  just  called  a  cat. 
In  other  words,  I  can't  predicate  an  individual  thing  of 
another  thing.  What  I  can  predicate  is  some  attribute 
of  the  thing.  But  attributes  are  of  two  kinds,  defining 
and  not-defining.  The  result  is  that  I  discover  the  fol- 
lowing division  of  attributes  :  — 

Attributes 
I 


defining  not-defining 

r r r 1 

generic  specific  proprium  accident 

(differentia) 

These  are  the  Five  Heads  of  Fredicables.  In  relation 
to  the  subject,  the  attributes  found  in  the  predicate  may 
be  generic,  specific,  differential,  a  constant  property, 
and  an  accident.  It  is  evident  that  these  terms  reflect 
classification  and  division,  and  this  fact  brings  out  once 
^  Macleane,  Season,  Thought,  and  Language^  p.  174. 


74  THE  ESSENTIALS  OF  LOGIC 

more  the  intimate  relation  between  the  ideal  form  of 
definition  and  these  processes. 

The  generic  attributes  give  the  connotation  of  the 
genus,  while  the  specific  attributes  are  those  which  are 
common  to  the  species.  It  will  be  remembered  that  the 
differentia  is  that  attribute,  or  attributes,  which  distin- 
guishes one  species  from  its  coordinate  species.  But 
an  object  may  possess,  besides,  some  property  not  es- 
sential enough  to  be  used  as  a  differentia  yet  always 
present.  When  this  property  is  deducible  from  the  de- 
fining attribute  it  is  called  a  'proprium.'  Attributes 
which  sometimes  belong  to  a  class  of  objects  and  are 
sometimes  absent  are  called  'accidents.'  It  is  an  acci- 
dent that  a  university  is  located  in  one  city  rather  than 
in  another ;  that  is,  it  is  no  part  of  the  nature  of  the 
university  to  have  this  particular  location.  It  is  an  ac- 
cident of  a  thief  to  be  in  prison  and  of  a  politician  to 
be  honest.  It  should  be  borne  in  mind,  however,  that 
the  term  is  here  used  in  connection  with  classification 
and  division.  In  another  sense  of  the  word  '  accident,' 
it  may  well  be  that  nothing  is  an  accident ;  this  means 
that  every  feature  of  an  individual  thing  has  a  cause. 

The  Importance  of  Definition.  From  its  very  be- 
ginning, logic  has  stressed  the  importance  of  definition. 
It  is  impossible  to  think  clearly  and  to  avoid  ambigui- 
ties without  definite  ideas  and  properly  applied  words. 
The  very  familiarity  of  words  may  lead  us  to  suppose 
that  we  understand  their  use,  and  encourage  us  in  the 
mere  manipulation  of  verbal  counters  to  the  neglect  of 
concepts.  Verbal  definition  is  important,  but  we  must 
never  forget  that  it  rests  upon  ordered  knowledge.  Or- 
dered knowledge  is,  however,  only  another  name  for 


PRINCIPLES  OF  DEFINITION  75 

real  dej&nition.  When  we  once  realize  this  fact,  we  im- 
mediately become  aware  of  the  importance  of  definition, 
both  as  a  process  and  as  a  result,  and  of  the  value  to 
the  individual  of  those  mental  habits  of  analyzing  and 
distinguishing  which  give  structure  and  clearness  of 
outline  to  his  accumulated  knowledge.  Definition  is  to 
the  mind  what  discipline  is  to  an  army.  Without  dis- 
cipline, an  army  is  like  a  mob ;  it  lacks  both  unity  and 
the  means  which  make  unity  effective.  Without  defini- 
tion, the  mind  lacks  differentiation  and  distinctness  in 
its  contents. 

REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  V. 
Davidson,  The  Logic  of  Definition,  cliap.  m. 
Hibben,  Logic,  Deductive  and  Inductive,  chap.  v. 
Jones,  Logic,  Inductive  and  Deductive,  chap.  rv. 
Macleane,  Reason,  Thought,  and  Language,  chap.  xi. 
Schiller,  Formal  Logic,  chap.  VL 


CHAPTER  VII 

ASSERTIONS  AND  PROPOSITIONS 

An  Important  Distinction.  As  logic  has  grown 
less  formal  and  has  been  more  influenced  by  psychology, 
it  has  more  and  more  recognized  the  necessity  of  draw- 
ing a  distinction  between  assertions  and  propositions. 
An  assertion  is  a  living  judgment  which  expresses  the 
conclusion  reached  by  an  individual  as  a  result  of  his 
thinking.  *  True  patriotism  stands  for  ideals,'  and,  '  I 
must  take  more  exercise,'  are  for  me  genuine  assertions 
which  I  understand.  But  when  I  glance  at  a  list  of  ex- 
ercises in  a  logic-text  and  come  across  the  sentence, '  It 
is  hot,'  I  am  not  absolutely  certain  what  '  it '  refers  to. 
I  tend  to  assume  that  the  weather  is  referred  to,  but 
the  writer  may  possibly  have  had  a  stove  or  a  cup  of 
tea  in  mind.  Such  isolated  sentences  need  interpreta- 
tion. The  reader  must  make  a  judgment  out  of  them 
by  his  own  mental  activity.  And,  as  we  all  know,  we 
are  sometimes  mistaken  even  when  the  context  is  quite 
complete.  In  contrast  to  personal,  living  assertions, 
then,  propositions  are  sentences,  or  verbal  complexes, 
which  are  supposed  to  symbolize  such  assertions ;  they 
are  bodies  into  which  some  mind  must  breathe  the 
breath  of  life.  Propositions  can  exist  on  paper,  while 
assertions  can  live  only  in  the  mind. 

Under  ideal  conditions,  the  propositions  put  forward 
in  actual  cases  of  argumentation  may  be  correct  substi- 
tutes for  assertions  quite  capable  of  conveying  to  other 


ASSERTIONS  AND  PROPOSITIONS  77 

minds  the  exact  shade  of  meaning  intended,  but  such 
is  not  always  the  case.  Before  this  transference  of 
meaning  from  one  mind  to  another  is  possible,  there 
must  be  painstaking  effort  on  the  part  of  the  listeners 
to  comprehend  those  who  are  speaking.  How  often  a 
statement  is  misunderstood,  or,  as  we  are  apt  to  say, 
twisted  and  distorted !  The  whole  context,  or  universe 
of  discourse^  must  be  appreciated  before  a  statement  is 
given  its  correct  setting.  Such  a  context  is  present  in 
any  actual  judgment,  but  it  cannot  be  attached  directly 
to  the  proposition.  A  sentence,  spoken  or  written,  can- 
not contain  very  much.  Take  the  famous  line  in  Shake- 
speare's Henry  VI:  "  The  Duke  yet  lives  that  Henry 
shall  depose  " ;  it  is  obvious  that  the  ambiguity  rests  in 
our  inability  to  get  to  the  real  assertion,  assuming  that 
there  was  one. 

When  conditions  are  very  favorable,  the  distinction 
between  assertions  and  propositions  can  be  allowed  to 
drop  into  the  background.  We  suppose  that  we  can 
pass  from  one  to  the  other  with  ease.  But  when  propo- 
sitions are  given  piecemeal  and  apart  from  their  con- 
text, it  is  often  impossible  to  interpret  them  in  any 
final  sense.  Under  such  conditions  we  are  forced  to  pay 
attention  to  certain  general  aspects  which  should  be 
clear.  We  change  propositions  into  assertions  as  com- 
pletely as  possible,  and  then  proceed  to  analyze  them. 
But  it  is  always  well  to  bear  in  mind  this  important 
distinction. 

Critical  vs.  Uncritical  Assertion.  Some  mental 
processes  are  relatively  unconscious,  while  others  de- 
mand attention  for  their  very  being.  We  often  act  and 
speak  habitually  and  imitatively.   We  do  what  we  have 


78  THE  ESSENTIALS  OF  LOGIC 

been  accustomed  to  do  and  to  see  others  do,  and  we  say 
things  which  couie  into  our  heads  or  which  we  have 
heard  other  people  say.  The  ideal  of  logic  is  to  make 
individuals  critical,  and  this  aim  is  furthered  by  the 
knowledge  it  gains  of  mental  processes  and  of  scientific 
methods.  But  when  logic  became  very  formal  and  gave 
almost  its  entire  attention  to  propositions  taken  sepa- 
rately, it  became  too  mechanical  to  help  the  individual 
in  his  concrete  thinking.  What  we  shaU  try  to  do,  then, 
is  to  explain  these  older  analyses  of  propositions  and 
give  them  a  more  vital  setting. 

Critical  thinking  seeks  to  determine  the  facts  and 
principles  of  the  case,  to  test  both,  and  then  to  see 
whether  the  conclusion  drawn  is  justified.  It  takes  as 
little  for  granted  as  possible.  It  brings  all  the  facts 
and  principles  into  the  open.  This  mental  effort  criti- 
cally to  interpret  a  case  of  reasoning  which  appears 
doubtful,  leads  to  the  marshaling  of  all  our  resources, 
to  the  bringing-out  of  all  the  facts  and  rules  which 
bear  upon  the  problem,  to  the  analysis  of  likenesses  and 
differences  with  other  cases,  to  the  more  patient  wait- 
ing for  suggestive  ideas.  The  result  is  usually  a  more 
adequate  solution  of  the  problem  with  a  broader  under- 
standing of  its  meaning.  Let  me  give  an  instance  of 
critical  versus  uncritical  thinking.  A  student  comes  to 
me  and  asks  whether  logic  is  a  practical  subject.  I 
know  pretty  well  by  past  experience  what  he  means  by 
the  term  '  practical.'  But  I  ask  him  and  he  replies,  '  Is 
it  of  use  in  everyday  life  ? '  Obviously,  by  everyday 
life  he  means  business  life.  Will  logic  help  him  to  suc- 
ceed in  his  profession?  It  thus  becomes  a  question  of 
the  qualifications  of  a  successful  business  man.    I  may 


ASSERTIONS  AND  PROPOSITIONS  79 

deny  that  his  ideal  of  success  is  a  wise  and  adequate 
one,  or  I  may  try  to  show  him  that  whatever  makes 
his  thinking  more  accurate  and  critical  has  a  tendency 
to  make  him  better  qualified  for  business.  The  student 
has  made  certain  assumptions  as  shown  by  the  very 
words  that  he  uses ;  in  fact,  he  has  revealed  an  outlook 
upon  life. 

What  is  an  Assertion  ?  We  may  define  an  asser- 
tion as  a  mental  act  and  content  arising  out  of  and 
concluding  a  jyrocess  of  interpretation.  Such  an  asser- 
tion is  a  judgment,  a  conclusion,  a  decision.  Interpre- 
tations, generalizations,  theories,  inferences,  beliefs, 
views,  decisions  are  present  from  the  early  days  of  a 
child's  life,  and  represent  the  growing,  synthetic  side 
of  its  mind.  The  growth  of  the  mind,  this  putting  two 
and  two  together,  this  recognizing  and  analyzing  and 
comparing,  is  not  a  mechanical  process.  It  is  remark- 
able how  soon  the  child  notices  things  and  seeks  to  in- 
terpret them.  A  little  girl  somewhat  less  than  three 
years  old  was  looking  at  her  teddy-bear  and  noted  for 
the  first  time  the  brown,  hairless  soles  of  its  feet.  The 
color  struck  her  attention  and  she  said,  "  That 's  blood." 
Her  brother,  aged  four,  gave  his  judgment.  "  No,  baby, 
that 's  where  the  whiskers  have  come  off."  Baby  re- 
plied, "  We  must  buy  some  at  the  store  and  put  them 
back  on." 

Of  much  of  this  continuous  interpretation  we  are 
not  reflectively  aware.  It  does  not  stand  out  so  clearly 
in  consciousness  that  we  remember  it  and  can  recall 
the  various  steps.  The  individual's  field  of  experience 
seems  to  him  always  to  have  been  much  the  same  as  it  is 
now.  Out  there  is  the  realm  of  physical  things  open  to 


80  THE  ESSENTIALS  OF  LOGIC 

inspection  ;  and  these  things  fall  into  kinds  which  are 
usually  easily  recognizable.  In  contrast  to  this  common 
world  of  physical  things  is  the  more  personal  domain 
of  the  self  with  its  feelings,  valuations,  and  purposes ; 
and  there  is,  finally,  the  social  realm  of  other  minds. 
In  other  words,  the  mind  of  each  individual  is  full  of 
implicit  assertions  which  cannot  be  accounted  for  apart 
from  pretty  constant  mental  activity.  Interpretation  is 
going  on  aU  the  time  and  finds  expression  in  judg- 
ments. These  judgments  are  assertions  which  deal  with 
these  recognized  realms.  When  I  say,  '  That 's  Smith,' 
I  mean  that  the  person  I  see  at  a  certain  distance  from 
me  goes  by  the  name  of  Smith.  When  I  say,  '  Nitrates 
are  necessary  for  the  soil  in  agriculture,'  I  take  the 
physical  world  for  granted  and  make  an  assertion  about 
certain  relations  between  it  and  plants.  Thus  we  are 
interested  in,  and  pass  judgments  about,  the  world  in 
which  we  live. 

Levels  of  Judgment.  We  have  taken  the  term 
*  Judgment '  in  a  broad  sense  as  standing  for  both  the 
process  and  the  act  of  interpretation.  Very  often,  the 
mental  steps  just  previous  to  the  assertion  do  not  rise 
to  the  surface  of  consciousness.  We  feel  certain  that 
the  person  over  yonder  is  Jones,  but  we  don't  just  know 
why.  He  gives  us  the  general  impression  of  Jones. 
Only  when  doubt  is  cast  upon  our  interpretation  of 
our  perception  do  we  look  more  closely  and  analyze 
this  feature  and  that  which  are  connected  in  our  mind 
with  Jones.  Perceptual  judgments,  or  judgments  bound 
up  very  closely  with  what  we  are  perceiving,  are  of  this 
almost  intuitive  character. 

The  more  of  a  problem  there  is,  the  more  reflective 


ASSERTIONS  AND  PROPOSITIONS  81 

is  judgment.  The  process  of  reaching  a  conclusion  now 
takes  time,  and  we  are  aware  of  various  suggestions  and 
steps.  We  try  to  find  exactly  what  is  given  and  where 
the  difficulty  lies,  and  then  ransack  our  experience  to 
find  a  satisfactory  solution.  Such  a  mental  process  is 
called  '  reasoning  '  and  may  take  a  long  time ;  but  when 
a  solution  is  found,  it  appears  as  a  judgment. 

It  is  customary  for  logicians  to  classify  judgments 
as  '  dominantly  perceptual '  or  as  *  dominantly  con- 
ceptual.' All  judgments  involve  concepts,  however,  and 
there  is  no  sharp  break  between  the  judgments  of  per- 
ception and  the  abstract  judgments  of  history  and  of 
science.  A  huge  body  of  facts  must  be  collected,  an- 
alyzed, compared,  and  organized  before  such  abstract 
judgments  are  possible.  In  the  latter  half  of  the  book 
we  shall  have  much  to  say  of  these  progressive  steps 
which  raise  us  to  such  abstract  judgments  as  '  The  plan- 
ets travel  in  elliptical  paths,'  and  '  Democracy  is  still  in 
process  of  development.' 

Concepts  and  Judgment.  Judgments  always  con- 
tain concepts,  or  meanings.  It  was  this  fact  that  led 
many  of  the  older  logicians  to  think  of  judgments  as 
formed  from  the  union  of  two  concepts.  That  is  now 
seen  to  be  too  mechanical  an  idea.  The  content  of  a 
judgment  is  complex,  but  it  is  also  unitary;  it  makes 
up  one  assertion. 

The  relation  between  concepts  and  judgment  is  a 
vital  one  and  can  be  understood  only  when  approached 
in  a  genetic  way.  Concepts  are  the  material  of  judg- 
ment and  are  at  the  same  time  products  of  judgment. 
To  ask  which  is  prior  in  any  absolute  way  is  like  ask- 
ing the  old  puzzle,  Which  came  first,  the  hen  or  the 


82  THE  ESSENTIALS  OF  LOGIC 

egg'f  Judgments  grow  out  of  conceptual  material,  but 
this  conceptual  material  is  itself  the  deposit  of  other 
judgments.  Again,  this  conceptual  material  is  modi- 
fied by  judging  as  a  process  and  exists  in  an  unique  way 
in  any  really  new  judgment.  An  example  may  make 
this  clearer. 

Take  a  person  who  is  visiting  an  aquarium  for  the 
first  time.  Undoubtedly,  he  has  some  idea  of  many  of 
the  kinds  of  fish  which  are  on  exhibit,  but  his  ideas  are 
usually  somewhat  vague  and  unsettled.  When  he  comes 
before  the  tank  in  which  is,  for  instance,  the  devil-fish 
or  ray,  he  makes  the  identification,  and,  in  so  doing, 
modifies  his  concept.  It  is  no  longer  the  hazy  concept 
it  once  was.  Again,  take  the  student  who  comes  to  col- 
lege. He  has  a  general  idea  of  what  a  college  is  for. 
But,  as  he  progresses  from  the  freshman  to  the  senior 
year,  he  is  compelled,  by  the  very  pressure  of  his  com- 
plex experience,  to  pass  judgments  in  which  this  gen- 
eral ideal  is  modified,  deepened,  and  enlarged.  Judg- 
ment is,  in  fact,  the  individual's  system  of  concepts  in 
process  of  adjustment  and  enlargement.  Concepts  drop 
into  the  background  so  far  as  consciousness  is  con- 
cerned and  become  potential  or  implicit  when  they  are 
not  the  living  parts  of  a  judgment. 

Judgment  defined.  There  are  many  definitions  of 
judgment,  varying  slightly  in  their  form  or  their  em- 
phases from  one  another.  Two  aspects  of  every  judg- 
ment stand  out  clearly.  There  is,  first,  the  complex 
content  which  is  held  before  the  mind,  and,  second,  the 
attitude  of  belief  or  acceptance  taken  toward  it.  Let 
us  look  a  little  more  closely  at  these  two  aspects. 

Every  judgment  involves  a  complex  content.   What 


ASSERTIONS  AND  PROPOSITIONS  83 

the  content  is  depends  upon  the  location  of  the  problem 
which  gives  rise  to  it.  It  may  be  dominantly  perceptual 
with  just  a  touch  of  conception  at  the  point  which 
needed  interpretation,  as  when  I  step  outdoors  of  a 
morning  and  exclaim,  '  It  's  a  fine  day  after  all ' ;  or  it 
may  be  almost  equally  perceptual  and  conceptual,  as 
when  I  classify  a  plant  which  I  run  across  in  my  stroll 
through  the  woods  ;  or  it  may  be  entirely  conceptual,  as 
in  the  statement  of  some  law  of  nature.  In  every  case, 
however,  the  total  content  which  I  hold  before  my 
mind  is  complex,  the  nature  of  the  complexity  varying 
with  the  field  involved  and  the  nature  of  the  problem 
to  which  the  judgment  is  an  answer.  Sometimes  we 
are  interested  in  the  qualities  of  things,  sometimes  in 
classes  and  their  relations  to  one  another,  sometimes  in 
comparisons,  sometimes  in  personages  and  events.  The 
character  of  the  content  determines  the  type  of  judg- 
ment with  which  we  have  to  deal. 

Again,  every  judgment  involves  a  mental  attitude 
which  is  that  of  belief  or  assertion.  As  a  rule,  the 
psychologist  prefers  the  term  '  belief,'  while  the  logician 
speaks  of  '  assertion.'  The  content  is  believed  or  asserted 
to  hold  of  the  realm  which  is  under  discussion.  When 
we  use  the  term  '  belief,'  we  keep  a  more  personal 
reference.  '  It  is  my  belief,  or  my  judgment,  that  Napo- 
leon was  a  worn-out  man  by  the  time  of  the  Russian 
campaign.'  Here  a  complex  idea  concerning  itself  with 
European  history  of  somewhat  over  a  century  ago  is 
accepted  as  true.  I  feel  constrained  by  the  pressure  of 
the  facts  to  think  of  Napoleon  in  this  way.  This  mental 
constraint  which  arises  out  of  the  facts,  says  the  logi- 
cian, leads  me  to  make  the  assertion,  '  Napoleon  was  a 


84  THE  ESSENTIALS  OF  LOGIC 

worn-out  man,'  etc.  Napoleon  and  the  Europe  of  Hs 
day  are  objects  before  my  mind's  eye,  and  I  determine 
to  think  of  one  feature,  which  has  been  open  to  ques- 
tion, in  this  way  rather  than  in  that.  The  rest  of  my 
knowledge  furnishes  the  setting  for  this  once  moot 
point  which  I  now  take  to  be  settled. 

!A  judgment  is,  then,  a  complex  mental  content  which 
is  asserted  or  toward  which  we  take  the  attitude  of 
belief.  Such  an  assertion  must  be  either  true  or  false. 
It  is  this  concern  with  truth  or  falsity  which  is  distinc- 
tive of  a  judgment.  In  language,  this  characteristic 
finds  expression  in  the  indicative  mood  in  contrast  to 
commands,  wishes,  and  questions.  The  reason  for  this 
difference  rests  ultimately  in  the  fact  that  knowledge 
is  claimed  or  assumed  in  the  one  form,  while  not  in 
the  others.  When  I  ask  a  question,  I  request  some  one 
else  to  make  an  assertion,  but  do  not  myself  make  one. 
When  1  issue  a  command,  1  am  concerned  with  an 
action  which  I  am  trying  to  bring  about.  In  neither 
case  am  I  expressing  a  belief. 

All  Knowledge  Judgmental  We  have  stressed 
the  fact  that  live  judgments  spring  from  problems.  But 
such  problems  must  always  be  local  or  concern  points  of 
doubt  within  a  larger  field  about  which  there  is,  for  the 
time  being,  no  question.  This  larger  field  which  fur- 
nishes the  setting  of  the  new  judgment  is  itself,  how- 
ever, the  product  of  the  continuously  accumulating 
judgments  of  the  mind  and  the  content  of  the  new 
judgment  is  knit  to  it  like  new  cells  in  a  growing  or- 
ganism to  the  old.  It  is  strictly  true  to  say  that  all  our 
knowledge  has  been,  at  one  time  or  other,  a  part  of  the 
content  of  a  judgment  and  that  it  is  more  or  less  im- 


ASSERTIONS  AND  PROPOSITIONS  85 

plied  as  a  foundation  for  the  new  judgment.  For  this 
reason  it  must  be  ready  to  defend  itself  and  to  pass 
from  a  potential,  or  passive  condition,  to  the  center  of 
the  mental  stage.  Each  of  us  possesses  a  system  of  con- 
cepts which  has  been  the  growth  of  years  of  guided 
and  unguided  mental  effort.  This  system  controls  our 
thinking  and  is  in  turn  controlled  by  it.  Only  a  small 
part  of  it  can  appear  overtly  in  the  field  of  attention  at 
any  one  time,  but  we  have  good  reason  to  believe  that 
all  of  it  is  there  in  a  more  or  less  effective  way. 

It  is  this  implication  of  a  larger  setting  for  any  new 
judgment,  a  setting  which  is  usually  more  implicit  than 
explicit,  that  the  philosophical  logician  always  stresses. 
And  it  is  well  to  remember  that  logic  is,  after  all,  a 
philosophical  discipline.  I  make  no  apology,  therefore, 
for  the  introduction  of  the  following  quotation  from 
Bosanquet :  "  We  may  then  sum  up  so  far :  our  knowl- 
edge, or  our  world  in  knowledge,  exists  for  us  as  a 
judgment,  that  is,  as  an  affirmation  in  which  our  present 
perception  is  amplified  by  an  ideal  interpretation  which 
is  identified  with  it.  This  interpretation  or  enlargement 
claims  necessity  or  universality,  and  is  therefore  objec- 
tive as  our  world,  i.e.,  is  what  we  are  obliged  to  think, 
and  what  we  are  all  obliged  to  think.  The  whole  system 
in  process  of  construction,  viz.,  our  present  perception 
as  extended  by  interpretation,  is  what  we  mean  by 
reality,  only  with  a  reservation  in  favour  of  forms  of 
experience  which  are  not  intellectual  at  all.  Every  judg- 
ment then  affirms  something  to  be  real,  and  therefore 
affirms  reality  to  be  defined,  in  part,  by  that  something. 
Knowledge  exists  in  the  form  of  affirmations  about 
reality.  And  our  world  as  existing  for  us  in  the  medium 


86  THE  ESSENTIALS  OF  LOGIC 

of  knowledge  consists,  for  us,  of  a  standing  affirmation 
about  reality."  ^ 

It  is  for  theory  of  knowledge  to  decide  the  character 
of  knowledge  and  its  relation  to  reality,  while  it  is  the 
function  of  metaphysics  to  determine  the  nature  of 
reality.  Logic  takes  both  knowledge  and  reality  for 
granted,  and  investigates  the  empirical  question  of  how 
knowledge  is  actually  built  up  and  sustained  by  human 
minds.  The  conclusion  which  is  forced  upon  us  is  that 
all  knowledge  is  judgmental  and  is  that  which  we  are 
constrained  to  think  by  the  pressure  of  our  experience. 

The  Part  played  by  Language.  The  actual  oper- 
ation of  judging  is  often  hard  to  recover.  The  modern 
logician,  working  hand  in  hand  with  the  psychologist, 
is  more  and  more  convinced  that  this  operation  is  not 
truly  reflected  in  the  verbal  form  which  is  called  the 
proposition.  So  far  as  consciousness  goes,  the  mental 
operation  is  usually  simpler  than  the  verbal  form. 
Language  is  more  analytic  and  detailed  than  the  think- 
ing of  any  one  moment.  There  are  two  reasons  for 
this.  Language  is  used  for  communication  and  re- 
flects all  the  distinctions  painstakingly  made  in  the 
past.  The  other  reason  lies  deeper,  language  is  a 
mechanism  and,  while  instrumental  to  thought,  is  not 
identical  with  it.  This  disunion  came  out  clearly  in 
several  of  the  preceding  chapters,  especially  in  the 
chapters  entitled  "  Ambiguity  and  Language "  and 
"  Principles  of  Definition."  It  would  be  impossible 
for  any  mechanism  to  equal  the  fluidity  and  organic 
unity  of  thought.  We  must  not  take  the  skeleton  for 
the  living  animal.  Consciousness  is  a  qualitative  com- 
^  The  Essentials  of  Logic,  p.  32. 


ASSERTIONS  AND  PROPOSITIONS  87 

plex  in  which  purpose,  context,  perception,  and  the 
whole  apperceptive  background  of  accumulated  ex- 
perience somehow  coexist  in  a  forward  movement  of 
interpretation.  Language,  on  the  other  hand,  is  spread 
out  in  space  and  time,  and  necessarily  adapts  itself  to 
this  process  of  extension.  TJw  purpose  of  language  is 
not  to  reflect  the  actual  genesis  of  a  thought^  hut  to 
express  the  result  in  a  comprehensible  way.  An  argu- 
ment should  be  capable  of  explicit  formulation  in  such 
a  way  as  to  give  the  conclusion  in  relation  to  its 
grounds.  So  far  as  logic  is  a  science  of  proof,  it  deals 
with  the  overt  and  not  with  the  hidden ;  and  the  overt 
must  find  expression  in  language. 

The  Logical  Treatment  of  Propositions.  Mod- 
ern logic  tries  to  be  as  concrete  and  flexible  as  possible. 
It  insists  upon  a  study  of  the  context  to  determine  the 
point  of  view  of  the  person  who  enunciated  a  given 
proposition.  But  within  such  a  setting,  or,  as  it  is 
called,  universe  of  discourse^  a  proposition  or  group  of 
propositions  is  a  bit  of  supposed  knowledge  which  has 
to  stand  by  itself  as  does  a  work  of  art  which  has  once 
left  the  atelier  of  the  master  for  the  gallery.  The 
proposition,  as  treated  by  the  logician,  is  an  instrument 
of  analysis  much  as  a  sensation  is  for  the  modem  psy- 
chologist. The  student  must  be  warned  that  the  tradi- 
tional analysis  of  the  proposition  to  which  we  now  pass 
is  dominated  by  the  mechanism  of  the  syllogism  and 
the  idea  of  class  relations  which  finds  expression  therein. 
For  this  reason,  the  *  logical  form '  of  propositions  is 
often  a  procrustean  bed  for  propositions  which  do  not 
naturally  express  class  relations.  The  art  side  of  logic 
will  come  to  the  fore  in  the  next  few  chapters. 


88  THE  ESSENTIALS  OF  LOGIC 

REFERENCES 

Bosanquet,  The  Essentials  of  Logic,  Lecture  iv. 
Dewey,  How  We  Think,  part  ii,  chap.  viii. 
James,  Principles  of  Psychology,  vol.  n,  chap.  xxi. 
Minto,  Logic,  Inductive  and  Deductive,  part  i,  chap.  n. 
Schiller,  Formal  Logic,  chap.  vin. 


CHAPTER  VIII 

THE  LOGIC  OF  PROPOSITIONS 

A  General  Division  of  Propositions.  Proposi- 
tions are  divided  into  '  categorical,'  '  hypothetical,'  and 
*  disjunctive.'  A  proposition  is  said  to  be  categori- 
cal when  it  makes  a  direct  assertion.  In  it  a  predicate 
is  denied  or  affirmed  of  a  subject.  '  The  Romans  were 
a  strong  race,'  and  '  Dead  men  don't  bite,'  are  examples. 
A  hypothetical  proposition  combines  a  condition  with 
a  consequent.  If  the  condition  is  fulfilled,  the  conse- 
quent is  held  to  be  true.  '  If  the  great  war  continues, 
the  nations  wiU  be  near  bankruptcy,'  and  '  If  there  is 
an  early  frost,  the  peach  crop  will  be  spoiled,'  are  cases 
in  point.  A  disjunctive  proposition  asserts  that  one  of 
two  or  more  alternatives  is  true.  '  Man  is  either  mortal 
or  immortal,'  and  '  This  rock  is  either  marble  or 
quartz,'  are  disjunctive  in  character. 

The  categorical  type  of  proposition  with  its  direct 
assertion  is  the  simplest  of  the  three  forms  and  is 
always  examined  in  logic  before  the  others.  It  is  the 
basis  of  the  categorical  syllogism.  We  shall  take  up 
the  other  types  for  discussion  afterwards. 

The  Quality  and  Quantity  of  Propositions.  Cate- 
gorical propositions  are  classified  according  to  quantity 
and  quality.  As  regards  quantity,  they  are  either  sin- 
gular, or  particular,  or  universal.  The  quantity  of  a 
proposition  is  an  aspect  of  the  subject  term.  If  the 
subject  denotes  only  one  individual,  the  proposition  is 


90  THE  ESSENTIALS  OF  LOGIC 

said  to  be  singular ;  if  it  denotes  all  the  members  of  a 
class,  universal ;  if  only  some  members  of  the  class  are 
denoted,  particular.  '  Abraham  Lincoln  was  a  sagacious 
statesman '  is  a  singular  proposition  because  the  subject 
term  denotes  only  one  individual.  '  Some  vines  bear 
edible  fruit '  is  a  particular  proposition  because  the 
subject  term  covers  only  a  part  of  the  class.  The  word 
*some,'  or  an  equivalent,  is  the  sign  of  a  particular 
proposition.  '  All  citizens  are  entitled  to  a  vote '  is  a 
universal  proposition.  Its  sign  is '  all '  or '  no '  ('  none  '), 
or  an  equivalent. 

The  quantity  of  a  proposition  is  not  always  definitely 
indicated  by  the  appropriate  logical  sign.  When  this 
is  the  case,  the  proposition  is  called  '  indefinite '  or 
*  preindesignate.'  The  first  task  of  the  logician  is  to 
determine  the  quantity  of  such  an  assertion,  for  a 
really  indefinite  proposition  is  ambiguous  and  can  have 
no  place  in  an  argument  until  its  ambiguity  is  removed. 
Since  the  mechanism  of  the  syllogism  stresses  quantity, 
it  is  absolutely  necessary  to  classify  an  assertion  before 
it  can  be  used  as  a  premise.  The  following  examples 
will  show  how  frequently  propositions  are  left  with 
their  quantity  implicit  and  even  uncertain  :  — 

'  Uneasy  lies  the  head  that  wears  a  crown.* 
'  Every  single  day  has  its  blessing.* 

*  All  flesh  is  not  the  same  flesh.' 
'The  race  is  not  always  to  the  swift.* 
•Haste  makes  waste.* 

*  A  man 's  a  man  for  all  that.' 


It  is  necessary  to  penetrate  beneath  the  verbal  form 
the  mea 
ject  term. 


to  the  meaning  and  decide  the  denotation  of  the  sub- 


THE  LOGIC  OF  PROPOSITIONS  91 

Quality^  when  applied  to  propositions^  is  a  term 
which  refers  to  their  character  as  affirmative  or 
negative.  An  affirmative  proposition  asserts  a  predi- 
cate of  a  subject,  while  a  negative  denies  it.  The 
distinction  is  too  familiar  and  ultimate  to  require  elu- 
cidation. There  are,  however,  certain  dangers  in  inter- 
pretation which  must  be  guarded  against.  The  mere 
presence  of  a  negative  word  in  a  proposition  does  not 
necessarily  make  it  negative  in  quality.  Such  a  word 
may  be  a  part  of  either  the  subject  or  the  predicate 
term.  Only  when  the  negative  element  involves  the 
assertion  of  a  relation  of  exclusion  between  the  com- 
ponent terms  is  the  quality  negative.  Take  the  prop- 
osition, '  Those  who  do  not  use  their  opportunities  are 
unwise.'  This  is  affirmative  in  quality  because  a  posi- 
tive relation  between  the  two  terms  is  asserted.  Whether 
the  subject  or  the  predicate  is  positive  or  negative  does 
not  affect  the  quality  of  the  proposition. 

Symbolic  Classification  of  Propositions.  For 
the  sake  of  easy  handling,  logic  has  classified  all  cate- 
gorical propositions  into  four  kinds  according  to  their 
quantity  and  quality.  This  treatment  has  the  syllogism 
for  its  end  in  view.  While  it  is  artificial  and  one-sided, 
^t  is  convenient  and  often  leads  to  a  better  understand- 
ing of  the  import  of  the  propositions.  These  four  kinds 
are,  '  universal  affirmative,'  '  universal  negative,'  '  par- 
ticular affirmative,'  and  '  particular  negative.'  To  sym- 
bolize these  the  vowels  A^  E^  /,  and  O  are  used.  A 
and  /stand  for  the  universal  and  particular  affirma- 
tive respectively,  and  are  taken  from  the  Latin  affirmo  ; 
E  and  O  stand  for  the  universal  and  particular  nega- 
tive, and  are  taken  from  nego.     It  should  be  noted 


92  THE  ESSENTIALS  OF  LOGIC 

that  the  singular  proposition  is  considered  a  universal. 
It  can  be  treated  as  such  in  the  syllogism.  Taking  S 
and  P  for  the  subject  terra  and  predicate  term  re- 
spectively, we  have  the  following  classification :  — 

^^  .  ,  (  Affirmative  :  All  S  ia  P.  A 

Universal  -  j^^g^^ive  :       No  S  ia  P.  E 


Particular  j 


Affirmative  :  Some  S  \a  P.  I 

Negative  :      Some  S  is  not  P.     O 


Reduction   of  Propositions  to  Logical  Form. 

The  reduction  of  the  varied  statements  of  ordinary  life 
to  a  form  corresponding  to  this  symbolism  is  a  practi- 
cal exercise  which  has  some  value.  How  much  it  is 
very  hard  to  tell.  "The  indirect  use  is  to  familiarize  us 
with  what  the  forms  of  common  speech  imply,  and  thus 
strengthen  the  intellect  for  interpreting  the  condensed 
and  elliptical  expression  in  which  common  speech 
abounds."  ^  Such  an  interpretation  is  often  difficult. 
For  instance,  it  is  not  always  easy  to  decide  whether  a 
sentence  is  particular  or  universal,  affirmative  or  nega- 
tive. Take  such  sentences  as  the  following  and  decide 
into  which  of  the  four  kinds  they  fall :  — 

•A  flower  is  a  beautiful  object.' 

*  Few  were  saved.' 

'  Women  are  jealous.' 

•  Only  ignorant  persons  hold  such  opinions.' 

The  reduction  of  statements  to  logical  form  meets 
with  three  classes  of  difficulties.  The  statement  may  be 
ambiguous  because  of  the  grammatical  order  of  its  parts 
or  because  of  the  character  of  certain  of  its  terms  ;  or 
it  may  contain  a  reference  to  time.  Let  us  look  at  these 
three  classes  in  some  detail. 

1  Minto,  Logic,  Inductive  and  Deductive,  p.  69. 


THE  LOGIC  OF  PROPOSITIONS  93 

The  order  of  subject  and  predicate  may  be  inverted. 
'  Wide  is  man's  mind  '  is  an  example  of  such  inversion. 
The  problem  is  so  simple  that  there  is  no  need  to  dwell 
on  it.  Again,  a  clause  may  be  separated  from  the  word 
it  modifies ;  for  example,  '  He  jests  at  scars  who  never 
felt  a  wound.'  In  such  cases  the  only  rule  is  to  pene- 
trate to  the  exact  meaning.  Lastly,  some  compound 
sentences  really  contain  more  than  one  proposition. 

In  the  second  class  come  partitive,  exclusive,  and 
exceptive  propositions.  A  partitive  proposition  is  one 
which  makes  a  statement  about  one  part  of  a  class  and 
implies  another  statement  about  the  rest.  There  is,  then, 
a  sort  of  double  meaning.  Such  words  as  '  all  .  .  .  not,' 
'  some,'  '  a  few,'  etc.,  involve  this  ambiguity  and  double 
significance.  '  All  these  children  are  not  of  school  age ' 
means  that  some  are  not,  and,  probably,  that  some  are. 
Accent  plays  some  part  here.  '  Few  are  chosen  '  means 
that  most  are  not  chosen. 

An  exclusive  proposition  is  one  which  is  introduced 
by  such  words  as  '  only,'  *  none  but,'  » alone,'  and  the 
like.  '  None  but  ticket-holders  are  admitted '  is  a  typi- 
cal exclusive  proposition.  This  means  that  all  those  who 
are  not  ticket-holders  are  not  admitted.  Thus  the  ref- 
erence is  to  those  who  do  not  belong  to  the  privileged 
class.  As  so  interpreted,  it  is  an  E  proposition.  But  it 
may  also  be  treated  as  an  A  proposition  by  interchanging 
subject  and  predicate :  '  All  who  are  admitted  are  ticket- 
holders.'  The  old  predicate  lies  within  the  subject-class. 
An  exceptive  proposition  is  one  which  makes  a  state- 
ment of  all  the  members  except  certain  designated  ones. 
Such  sentences  are  introduced  by  such  expressions  as 
*  all  but,'  '  all  except,'  etc.    '  All  but  the  very  poor  enjoy 


94  THE  ESSENTIALS  OF  LOGIC 

liberty'  is  an  example.  Two  statements  are  usually  in- 
volved :  '  All  who  are  not  very  poor  enjoy  liberty,'  and 
'  All  who  are  very  poor  do  not  enjoy  liberty.'  The  first 
of  these  is  more  certainly  implied  than  the  second.  It 
is  therefore  best  to  restate  the  proposition  dropping  out 
the  exceptive  particle. 

The  third  class  of  difficulties  is  technical  in  character. 
The  logical  form,  '  S  is  jP,'  is  the  statement  of  a  rela- 
tion between  classes  and  does  not  express  either  time  or 
modality.  The  customary  way  is  to  throw  this  verbal 
element  into  the  predicate.  Thus,  '  The  soldiers  had 
retreated '  becomes  '  The  soldiers  are  in  the  class  of 
those  who  had  retreated,'  and  'It  may  rain '  becomes 
'  Raining  is  an  event  which  may  occur.'  When  we  are 
trying  to  bring  out  class  relationships,  we  must  not  be 
affrighted  by  the  clumsiness  of  the  result. 

The  Distribution  of  Terms.  The  logical  form 
stresses  the  denotation  of  the  subject  and  predicate 
terms.  If,  in  a  proposition,  an  assertion  is  made  about 
the  entire  denotation  of  a  class,  the  terra  indicating  that 
class  is  said  to  be  '  distributed  ' ;  if  it  is  made  of  only  a 
part  of  the  class,  the  term  is  '  undistributed.'  The  dis- 
tribution of  the  terms  in  the  four  kinds  of  categorical 
propositions  has  been  worked  out  and  is,  besides,  pretty 
obvious.  ITie  universal  affirmative  distributes  only  the 
subject  term.  Thus  in  the  sentence,  '  All  mammals  are 
vertebrates,'  the  assertion  is  made  of  every  mammal, 
but  there  is  no  corresponding  reference  to  the  whole 
class  of  vertebrates.  We  have  the  right  to  say  only  that 
some  vertebrates  are  mammals.  The  particular  affirm- 
ative distributes  neither  the  subject  nor  the  predicate 
term.    '  Some  men  are  loyal '  is  an  /  proposition,  and 


THE  LOGIC  OF  PROPOSITIONS  95 

there  is  in  this  no  reference  to  the  entire  denotation  of 
either  class.  Turning  to  negative  propositions,  we  find 
that  an  E  proposition  distributes  both  terms.  Both 
terms  are  entirely  excluded  from  one  another,  and  this 
means  that  there  is  some  knowledge  about  all  the  mem- 
bers of  both  classes,  just  enough  to  validate  this  exclu- 
sion. '  No  man  is  perfect '  informs  us  that  not  a  single 
man  is  perfect,  and  that  not  a  single  perfect  being  is  a 
man.  Lastly,  an  O  proposition  distributes  the  predi- 
cate  and  does  not  distribute  the  subject.  '  Some  men 
are  not  honest '  tells  us  something  only  about  some  men, 
but  we  must  know  something  about  all  individuals  who 
are  honest  in  order  to  know  that  some  men  are  totally 
excluded.  Examining  the  distribution  of  the  terms  in 
the  four  kinds  of  propositions,  we  find  the  following 
rule :  negative  propositions  distribute  tlieir  predicates, 
while  affirmative  propositions  distribute  only  the  sub- 
ject and  this  only  when  the  proposition  is  universal. 

The  Graphical  Method.  The  relation  between  the 
subject  and  the  predicate,  as  regards  their  denotation 
and  the  distribution  of  each  term,  can  be  graphically 
represented  for  the  four  kinds  of  propositions  by  Euler's 
method.  If  each  term  be  represented  by  a  circle,  the 
result  is  as  follows :  For  A,  — 
/S,  the  subject  class,  is  seen  to  fall  en- 
tirely within  P^  the  pred- 
icate class,  for  the  vast 
majority  of  cases.  (Fig. 
1.)     Only  in  the  case  of  ^'  ' 

definitions,  in  which  the  two  classes  co- 
Fig.  2.  iucide,  do  we  find  the  relation  that  of 

Fiff.  2.    The  shadins:  shows  the  distribution. 


96 


THE  ESSENTIALS  OF  LOGIC 


For  E,  — 


Fig.  3. 

S  falls  entirely  outside  P.  Both  terms  are  distributed. 
For  /,  — 


Fig.  4. 


S  and  P  overlap.  Neither  term  is  distributed. 
For  0,— 


Fig.  6. 

some  S  is  known  to  be  excluded  by  P.  The  predicate 
term  is  distributed. 

Euler's  method  is  applicable  to  the  syllogism  also. 
Hence  it  is  well  to  become  familiar  with  this  graphical 
treatment  of  the  denotative  aspect  of  propositions. 

The  Purpose  of  Logical  Analysis.  This  manipu- 
lation of  sentences  will  undoubtedly  strike  the  reader 
as  artificial.   When  we  say,  '  All  men  are  mortal,'  we 


THE  LOGIC  OF  PROPOSITIONS  97 

do  not  mean  that  men  are  in  the  class  of  mortal  beings. 
We  think  of  the  predicate  in  its  connotation  rather  than 
in  its  denotation.  But  there  is  a  purpose  back  of  this 
stress  upon  denotation  and  class  relationships,  that  of 
syllogistic  analysis  and  testing.  The '  logical  form '  is  the 
syllogistic  form.  When  the  modern  logician  is  not  in- 
tent upon  proof,  he  tries  to  understand  the  exact  shade 
of  meaning  and  the  exact  character  of  the  relation  pres- 
ent in  a  proposition.  He  seeks  to  classify  propositions 
into  natural  types  corresponding  to  levels  qf  knowledge 
and  reflection.  But  as  a  syllogizer,  he  is  a  specialist  in- 
tent upon  his  method  and  bending  everything  to  it.  He 
then  selects  one  aspect  of  propositions  and  moulds  them 
in  such  a  way  as  to  bring  out  this  aspect  most  clearly. 
*A11  /S'is  P'  means  that  'All  S  is  contained  in  P.' 
It  is  the  denotation  of  related  classes  that  he  has  in 
mind.  For  a  few  chapters  we  shall  be  dominated  by  this 
purpose,  and  the  student  should  bear  this  fact  in  mind 
if  he  cannot  always  see  the  importance  of  certain  rather 
formal  processes.  The  means  secure  their  value  from  the 
end  and  are  as  valuable  as  the  end.  But  it  can  further 
be  said  that  the  thorough  study  of  the  denotative  aspect 
of  categorical  propositions  cannot  help  but  increase  our 
imderstanding  of  their  reach  and  meaning. 

REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  vi. 

Jones,  Logic,  Inductive  and  Deductive,  chap.  v. 

Keynes,  Formal  Logic,  part  ii,  chap.  i. 

Miuto,  Logic,  Inductive  and  Deductive,  part  I,  chap.  n. 

Taylor,  Elementary  Logic,  chap.  vii. 


CHAPTER  IX 

THE  IMPLICATIONS  OF  PROPOSITIONS 

Immediate  Inference.  Since  the  proposition  is  for 
the  logician  the  unit  of  knowledge,  he  wishes  to  ex- 
haust its  meaning.  He  studies  a  proposition  with  the 
express  purpose  of  finding  out  all  that  it  implies.  Now, 
it  has  been  found  that  we  can  pass  from  one  proposi- 
tion to  others  containing  the  same  two  terms  or  their 
contradictories.  Thus,  'AH  men  are  rational'  enables 
us  to  say  also  that  '  No  men  are  irrational '  and  '  No 
irrational  beings  are  men.'  Such  a  passage  from  one 
proposition  to  others  is  called  '  immediate  inference.' 
The  logician  has  usually  been  less  concerned  with  the 
mental  processes  involved  than  with  the  validity  and 
formal  mechanism  of  the  step. 

Let  us  recall  the  distinction  between  a  judgment  and 
a  proposition.  A  proposition  is  the  verbal  expression 
of  a  judgment.  It  is  usually  more  stereotyped  than  the 
living  judgment  and  practically  always  stresses  some 
one  aspect  of  the  situation  to  the  exclusion  of  others. 
Once  a  proposition  is  formulated,  however,  we  can  go 
back  over  it  and  analyze  it,  turn  it  about  and  see  it 
from  different  angles.  Thus,  when  I  make  the  asser- 
tion, '  This  book  is  on  the  desk,'  I  can  afterwards  note 
that  'The  desk  must  be  under  the  book.'  Such  a 
spatial  relation  has  a  double  direction.  Only  one  di- 
rection is  brought  out  in  the  original  proposition,  but 
I  realize  that  the  other,  also,  exists.  In  like  manner,  as 


THE  IMPLICATIONS  OF  PROPOSITIONS       99 

we  shall  see,  the  logical  form  to  which  the  logician  re- 
duces categorical  propositions  stresses  a  relation  be- 
tween terms  and  the  denotation  of  these  terms.  The 
consequence  is  that  other  propositions  can  be  seen  to 
follow  from  any  one  formulation. 

But  because  other  propositions  can  be  asserted  on 
the  basis  of  a  given  proposition,  it  does  not  foUow  that 
these  other  propositions  present  themselves  without  any 
mental  effort  on  the  part  of  the  thinker.  Immediate; 
inference  is  not  immediate  in  the  sense  that  it  is  intui- 
tive. The  nature  of  the  relations  must  be  clearly  grasped 
before  such  implications  can  be  quickly  drawn.  It  is 
for  this  reason  that  logical  analysis  is  of  value.  Only 
one  who  has  mastered  this  analysis  can  answer  such 
questions  as  those  given  at  the  end  of  the  chapter. 
Why,  then,  does  the  logician  speak  of  the  development 
of  the  implications  of  propositions  as  '  immediate  infer- 
ence '  ?  Because  he  has  in  mind,  as  a  contrast,  the  draw- 
ing of  a  conclusion  from  the  putting  together  of  two 
other  propositions  called  'premises.'  In  other  words, 
the  historical  contrast  is  with  the  syllogism  and  its  dif- 
ferent mechanism. 

There  areybwr  headings  under  which  different  kinds 
of  immediate  inference  are  brought :  ♦  Opposition,' 
*  Conversion,'  'Obversion,'  and  'Contraposition.'  We 
shall  now  examine  these  in  order  and  as  briefly  as  is 
consonant  with  completeness  and  clearness. 

The  Oppositions  of  the  Four  Kinds  of  Propo- 
sitions. Propositions  are  said  to  be  opposed  when  they 
have  the  same  terms  as  subject  and  predicate,  but  dif- 
fer in  quantity,  or  in  quality,  or  in  both.  Within  the 
setting  given  by  the  logic  of  propositions,  we  are  able 


100 


THE  ESSENTIALS  OF  LOGIC 


Contrariea 


\c 


t: 

8» 


^^. 


<* 

v 


\ 


X 


/ 


to  note  certain  relations  of  inclusion  and  exclusion 
which  such  statements  bear  to  one  another.  The  study 
of  these  relations  will  give  us  a  better  idea  of  the  reach 
of  each  kind  of  proposition.  It  will  likewise  teach  us 
how  to  establish  each  kind  and  what  its  denial  implies. 
If  the  symbols  of  the  four  kinds  of  propositions  be 
placed  at  the  four  comers  of  a  square  with  the  uni- 
versal at  the  top  and  the  corresponding  particulars  at 
the  bottom,  we  shall  obtain  the  so-called  '  Square  of 

Opposition.'  The 
sides  and  diago- 
nals of  this  square 
represent  relations 
between  A,  £J,  /, 
and  O.  Close  in- 
spection has  re- 
vealed four  kinds 
of  relation  among 
them :  — 

A  and  ^  are 
called  'contraries.' 
They  differ  in  qual- 
ity while  the  same 
in  quantity,  both  being  universal.  If  we  examine  them 
in  relation  to  each  other,  we  find  that  both  may  be 
false  while  only  one  can  be  true.  Thus,  'AH  swans 
are  white'  and  'No  swans  are  white'  are  contraries. 
They  cannot  both  be  true,  yet  they  may  both  be  false. 
As  a  matter  of  fact,  we  know  that  some  swans  are 
white  while  others  are  black. 

A  and  O,  B  and  /,  are  called  '  contradictories.'  They 
differ  in  both  quantity  and  quality.  Thus  the  members 


X>' 


Subconf raries 


O 


Fig.  6. 


THE  IMPLICATIONS  OF  PROPOSITIONS     101 

of  these  couples  are  exact  opposites.  One  must  he  true 
and  the  other  false.  '  All  politicians  are  honest '  and 
'  Some  politicians  are  not  honest '  are  contradictories. 
They  cannot  both  be  true  nor  both  false.  It  follows 
that  the  assertion  of  /  involves  the  denial  of  jE',  and 
the  denial  of  A  the  assertion  of  O. 

I  and  O  are  called  '  subcontraries.'  They  agree  in 
quantity  and  diflfer  in  quality.  Both  may  he  true,  hut 
hoth  cannot  he  false.  '  Some  men  are  brave '  and  *  Some 
men  are  not  brave '  are  subcontraries.  Our  experience 
tells  us  that  both  these  propositions  are  true.  When, 
however,  we  are  able  to  state  a  universal,  the  one  sub- 
contrary  is  true,  while 'the  other,  which  is  the  contra- 
dictory of  the  universal,  is  false. 

A  and  /,  £J  and  O,  are  called  '  subalterns.'  They 
agree  in  quality,  but  differ  in  quantity.  Subalterns  are 
both  true  when  the  universal  is  true.  When  the  con- 
trary universal  is  true,  both  subalterns  are  false.  '  All 
men  are  rational '  and  '  Some  men  are  rational '  are 
subalterns. 

It  is  a  good  exercise,  to  test  the  recognition  of  these 
interrelations,  to  start  with  the  truth  of  any  one  kind 
of  proposition  and  determine  what  follows  for  the  other 
three.  Granted  ^,  /  must  be  false  as  its  contradictory, 
0  must  be  true  as  its  subaltern,  and  A  must  be  false 
as  its  contrary.  If  we  deny  J^,  we  automatically  affirm 
/.  It  should  be  noted  that  common  speech  talks  of 
contradiction  whether  we  affirm  the  contrary  or  the 
contradictory  of  a  given  proposition.  It  is,  however, 
convenient  to  have  the  two  terms  for  these  oppositions. 
Both  are  opposed  to  the  given  proposition,  but  the  con- 
trary is  harder  to  establish  than  the  contradictory. 


102  THE  ESSENTIALS  OF  LOGIC 

Conversion.  Conversion  is  the  process  of  inter- 
changing subject  and  predicate  while  the  quality  of 
the  proposition  remains  the  same.  '  No  man  is  perfect ' 
becomes  'No  perfect  being  is  a  man.'  The  original 
proposition  is  called  the  '  convertend '  and  the  new  one 
the  '  converse.' 

We  must  not  forget  that  in  conversion  we  are  deal- 
ing with  propositions  which  have  been  reduced  to  logical 
form  and  that  the  relation  stressed  is  that  of  the  deno- 
tation of  the  class  terms.  This  relation  is  mutual.  The 
situation  is  analogous  to  the  arithmetical  relation  of 
equality  between  two  quantities.  If  ^  =  ^,  then  B  = 
A.  If  /S'  is  contained  in  P,  P  is  to  some  extent  con- 
tained in  S. 

The  rule  of  conversion  is  that  no  term  may  be  dis- 
tributed in  the  converse  which  was  not  distributed  in 
the  convertend.  The  reason  for  this  rule  is  obvious.  A 
violation  of  it  would  involve  making  an  assertion  not 
justified  by  the  denotation  given  in  the  original  propo- 
sition. We  should  be  going  beyond  our  data. 

There  are  two  kinds  of  conversion  :  (a)  simple  con- 
version ;  (6)  conversion  by  limitation,  or  per  accidens. 
Simple  conversion  is  the  mere  exchange  of  subject  term 
and  predicate  term.  E  and  /  can  be  converted  simply. 
Thus,  '  No  men  are  unaffected  by  self-interest '  becomes 
'No  individuals  unaffected  by  self-interest  are  men.' 
Both  terms  are  distributed  in  the  converse,  but  they 
were  already  distributed  in  the  convertend.  Hence  the 
rule  is  not  violated.  '  Some  men  are  honest '  becomes  - 
'  Some  honest  beings  are  men.'  Both  terms  are  undis- 
tributed in  the  first  as  in  the  second  proposition.  A 
must  be  converted  by  limitation.  Thus,  '  All  voters  are 


THE  IMPLICATIONS  OF  PROPOSITIONS     103 

citizens '  becomes  '  Some  citizens  are  voters.'  In  con- 
verting a  universal  affirmative,  we  are  forced  to  pass 
from  A  to  an  /.  It  will  be  remembered  that  the  predi- 
cate of  an  affirmative  proposition  is  undistributed. 

We  have  pointed  out  how  £J,  A^  and  /  can  be  con- 
verted. There  remains  O.  But  O  cannot  be  converted 
because  the  result  of  an  attempt  would  violate  the  rule. 
The  undistributed  subject  term  would  become  the  predi- 
cate of  a  negative  proposition  and  hence  automatically 
claim  distribution.  The  only  way  to  interchange  sub- 
ject and  predicate  in  the  case  of  an  O  proposition  is  to 
obvert  first  and  then  convert.  This  double  process  is 
called  'contraposition.'  Before  we  pass  to  it,  we  must 
examine  obversion. 

Obversion.  Obversion  is  the  process  oj^  changing 
the  quality  of  a  proposition  while  retaining  its  mean- 
ing. We  may  wish  to  state  an  affirmative  proposition 
in  its  corresponding  negative  form,  or  vice  versa.  When 
this  is  the  case,  we  must  obvert.  Which  form  is  first 
used  depends  upon  the  purpose  and  psychological  setting. 
But  it  is  often  convenient  to  restate  the  proposition  so 
as  to  bring  out  another  emphasis.  The  mechanism  of 
the  syllogism,  also,  makes  it  preferable  at  times  to 
change  the  quality. 

The  method  of  obversion  is  to  take  the  contradictory, 
or  negative,  of  the  predicate  and  then  change  the  quality 
of  the  proposition.  Its  principle  is  that  the  denial  of 
the  contradictory  of  a  predicate  is  the  same  as  the  affir- 
mation of  the  predicate,  and  the  affirmation  of  the  contra- 
dictory the  same  as  the  denial  of  the  original  predicate. 
No  mistake  must  be  made  in  taking  the  exact  opposite, 
or  contradictory,  of  the  predicate.  The  contradictory  of 


104  THE  ESSENTIALS  OF  LOGIC 

a  negative  predicate  gives,  of  course,  a  positive  term. 
Let  us  take,  fii'st,  the  symbolic  logical  form, '  All  Sis  P^ 
and  obvert  in  order  to  show  the  mechanism  of  the  proc- 
ess. P  becomes  not-P,  the  quality  is  changed,  and  the 
proposition  becomes  *  No  S  is  not-P.'  The  proposition 
*  None  of  the  crew  were  saved '  becomes  '  All  of  the  crew 
were  individuals  who  were  not  saved,'  which,  rendered 
into  good  English,  is,  *  All  of  the  crew  perished.' 

The  following  examples  may  make  this  discussion  of 
principle  and  method  clearer :  — 

A,  'AH  the  people  were  rescued,'  becomes,  E,  'None  of  the 
people  were  lost.' 

E,  '  No  practical  men  are  poets,'  becomes.  A,  '  All  practical  men 
are  not-poets.' 

/,  '  Some  vegetables  are  edible,'  becomes,  0, '  Some  vegetables 
are  not  inedible.' 

O, '  Some  houses  are  not  beautiful,'  becomes,  /, '  Some  houses 
are  ugly.' 

The  student  must  be  on  his  guard  against  two  things : 
misinterpretation  of  the  original  proposition,  the  obver- 
tend,  and  the  wrong  treatment  of  the 
predicate. 

The  principle   of   obversion   can  be 
represented  graphically  by  means  of  a 
circle   divided  into  two  compartments. 
Fig.  7.  (See  fig.  7). 

"  Then  any  given  thing  will  fall  into  one  or  other 
of  those  compartments.  If  our  proposition  asserts  that 
it  falls  into  one,  that  is  tantamount  to  asserting  that  it 
falls  outside  the  other :  the  latter  assertion  would  be 
the  obverse  of  the  former.  S  is  P,  implies  that  S  is  not 
not-P;  Tis  not-P,  implies  that  Tis  not  P."i 
1  Jones,  Logic,  Inductive  and  Deductive^  p.  122. 


THE  IMPLICATIONS  OF  PROPOSITIONS     105 

False  Obversion.  In  valid  obversion,  the  contradic- 
tory of  the  predicate  is  affirmed  or  denied,  as  the  case 
may  be,  of  the  original  subject.  We  have  just  noted  the 
theory  of  such  a  change  of  quality. 
The  universe  is  divided  into  P  and 
not-i-*,  and  to  affirm  one  is  the  same 
as  to  deny  the  other.  This  is  the  so- 
called  'law  of  counter-indication.' 
But  this  law  does  not  hold  of  the 
subject  in  its  relation  to  the  predi- 

1  1  T  -1  Fig.  8. 

cate  because  the   predicate   is  the 

larger  term.    If  all  S  \s>  P^  it  does  not  follow  that 

no  not->S'  is  jP,  as  can  be  seen  from  the  use  of  Euler's 

circles. 

An  example  of  false  obversion  may  make  this  situa- 
tion clearer.  Take  the  proposition,  '  All  who  are  con- 
nected with  this  affair  are  honest.'  Valid  obversion 
would  give,  '  None  who  are  connected  with  this  affair 
are  dishonest,'  while  false  obversion  would  give,  '  None 
who  are  not  connected  with  this  affair  are  honest.'  It 
is  obvious  that  the  last  proposition  is  not  the  equivalent 
of  the  other  two. 

Contraposition.  Contraposition  is  a  process  which 
combines  obversion  and  conversion.  Thus  the  quality 
of  the  proposition  is  changed  and  its  terms  are  inter- 
changed. '  No  voters  are  aliens '  becomes  by  obversion, 
*  All  voters  are  not-aliens  (citizens),'  and  this,  by  con- 
version, becomes, '  Some  not-aliens  (citizens)  are  voters.' 
No  new  principle  is  raised  by  contraposition.  The  prac- 
tical difficulty  is  to  keep  the  first  step  clearly  in  mind 
while  passing  to  the  second.  Inspection  shows  that  the 
contrapositive  has  for  its  subject  the  contradictory  of 


106  THE  ESSENTIALS  OF  LOGIC 

the  original  predicate,  while  the  quality  is  changed. 
This  manipulation  has  value  especially  for  the  0  propo- 
sition. It  will  be  remembered  that  an  O  statement 
cannot  be  converted  because  of  the  lack  of  distribution 
of  the  subject.  By  obversion  O  becomes  /,  and  this  can 
be  converted  simply.  For  example,  '  Some  men  are  not 
inventors '  becomes,  successively,  '  Some  men  are  indi- 
viduals who  are  not  inventors '  and  '  Some  individuals 
who  are  not  inventors  are  men.' 

Significance  of  Immediate  Inference.  The  stu- 
dent can  now  better  judge  for  himself  the  significance 
of  immediate  inference.  Does  he  understand  more  com- 
pletely the  meaning  of  propositions  when  he  can  work 
out  their  implications  ?  The  processes  are  not  hard  to 
master  and  do  repay  attention.  He  who  has  mastered 
them  does  not  have  to  guess  whether  one  proposition  is 
or  is  not  equivalent  to  another.  On  the  technical  side, 
these  processes  are  analogous  to  mental  arithmetic,  and, 
since  they  are  always  combined  with  the  problem  of 
reduction  to  logical  form,  give  valuable  discipline.  The 
thinker  must  be  in  a  position  to  handle  propositions 
skillfully  and  correctly  if  he  wishes  to  analyze  and  test 
his  conclusions  and  those  of  others. 


REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  V. 
Creighton,  An  Tntroditctory  Logic,  chap.  vn. 
Jones,  Logic,  Inductive  and  Deductive,  chap,  vn., 
Keynes,  Formal  Logic,  chaps,  n,  m,  and  iv. 


CHAPTER  X 

THE  SYLLOGISM  AS  A  MECHANISM 

The  Nature  of  the  Syllogism.  The  syllogism  was 
the  discovery  of  Aristotle,  that  is,  he  was  the  first  to 
work  out  its  theory  and  its  rules.  His  own  definition 
should  therefore  serve  very  weU  to  introduce  us  to  a 
brief  study  of  its  nature.  In  the  Prior  Analytics,  he 
offers  the  following  broad  one :  "  Discourse  in  which 
certain  things  being  posited,  something  else  than  what 
is  posited  necessarily  follows  on  their  being  true."  To 
syllogize  is  to  reason  things  together  and  draw  a  neces- 
sary conclusion.  But  when  we  examine  the  Aristotelian 
syllogism  more  closely  and  see  it  in  its  context,  we  real- 
ize that  this  definition  is  too  broad.  There  is  necessary 
reasoning  which  is  not  syllogistic.  What,  then,  is  the 
differentia  ?  This  is  to  be  found  in  the  character  of  the 
things  posited.  A  syllogism  is  a  discourse,  or  argu- 
ment, in  which  three  propositions  are  so  related  that 
one  of  them  (the  conclusion')  follows  from  the  other 
two.  The  germ  of  the  invention  was  the  analysis  of 
propositions  into  terms.  The  syllogism  was  conceived 
by  Aristotle  as  a  reasoning  together  of  terms.  His 
prime  discovery  was  that  whenever  two  propositions 
necessarily  contain  or  imply  a  conclusion  they  have  a 
common  term,  that  is,  only  three  terms  between  them.^ 
In  the  last  few  chapters  we  have  studied  propositions 
separately,  analyzing  them,  working  out  their  implica- 
^  Minto,  Logic,  Inductive  and  Deductive,  p.  170. 


108  THE  ESSENTIALS  OF  LOGIC 

tions,  reducing  them  to  logical  form.   Now  we  must 
consider  their  interdependence. 

A  single  proposition  taken  by  itself  is  an  assertion 
which  does  not  give  its  ground.  When  it  is  advanced 
by  a  person  other  than  ourselves,  we  are  almost  sure 
to  demand  why  this  conclusion  is  reached  rather  than 
another.  In  other  words,  we  want  the  assertion  con- 
nected with  some  generally  accepted  principle  as  its 
consequence  before  we  are  inclined  to  give  it  assent. 
This  backward  movement  to  more  basic  propositions  is 
characteristic  of  the  syllogism,  and  gives  us  a  clue  to 
its  purpose :  it  is  an  instrument  of  testing  rather  than 
an  instrument  of  discovery.  I  would  not  say  that  it 
never  leads  to  new  conclusions,  but  it  is  primarily  a 
method  of  determining  the  consistency  of  propositions 
already  thrown  out  for  acceptance.  There  has  been 
much  misunderstanding  on  this  point  both  now  and  in 
the  past.  John  Locke  was  protesting  against  the  idea, 
commonly  enough  held  in  his  day,  that  men  should  do 
their  creative  thinking  in  terms  of  the  syllogism,  when 
he  made  the  oft-quoted  gibe,  "  God  has  not  been  so 
sparing  to  men,  to  make  them  barely  two-legged  crea- 
tures, and  left  it  to  Aristotle  to  make  them  rational." 
Even  to-day  there  are  not  wanting  psychologists  who 
are  at  great  pains  to  demonstrate  that  the  syllogism  is 
not  an  adequate  description  of  how  reasoning  actually 
takes  place  in  human  minds.  But  any  argument  should 
be  capable  of  being  thrown  into  the  syllogistic  form  or 
something  analogous  to  it  for  purposes  of  testing  its 
validity  and  assumptions.  If  the  conclusion  follows  nec- 
essarily from  other  propositions,  the  argument  is  valid 
or  self -consistent.   The  conclusion  need  not,  however,  he 


THE  SYLLOGISM  AS  A  MECHANISM        109 

true.  Only  if  the  other  propositions,  from  which  it  is  a 
valid  deduction,  are  true,  is  it  true. 

Thus,  the  syllogism  is  an  instrument  which  plays  a 
part  within  a  larger  whole,  that  of  experience  and  re- 
flection. When  we  come  to  study  the  logic  of  science, 
we  shall  better  understand  whence  the  propositions 
come  which  appear  in  the  syllogism.  The  main  point  to 
realize  now  is  that  the  syllogism  cannot  prove  their 
truth  and  does  not  try  to ;  what  it  does  try  to  prove,  and 
can  prove,  is  the  consistency  or  inconsistency  of  their 
interrelations. 

An  Analysis  of  the  Syllogism.  Having  got  a  clear 
idea  of  the  nature  and  work  of  the  syllogism,  we  can 
now  describe  it.  It  is  a  very  simple  bit  of  mechanism 
resting  on  the  analysis  of  propositions  into  their  logical 
form  as  assertions  or  denials  of  relation  between  the 
denotation  of  classes.  This  relation  to  which  attention 
is  directed  is  that  of  inclusion  and  exclusion.  It  will  be 
recalled  that  an  A  proposition  is  symbolized  thus  :  '  All 
S  is  contained  in  P.''  Now,  Aristotle  saw  that  two 
terms  could  be  combined  in  a  proposition  as  a  result  of 
their  relation  to  a  third  term.  The  following  typical 
syllogism  will  illustrate  this  simple  underlying  idea :  — 

All  men  are  mortal; 
Socrates  is  a  man; 
Therefore  Socrates  is  mortal. 

The  three  terms  are, '  Socrates,' '  mortal,'  and  *  man.* 
It  is  evident  that  '  Socrates '  and  '  mortal,'  the  two 
terms  brought  together  in  the  conclusion,  are  estab- 
lished in  their  relation  by  means  of  a  third  term  to 
which  both  are  related.  What  is  the  character  of  this 
relation  which  holds  between  these  terms  and  makes 


110  THE  ESSENTIALS  OF  LOGIC 

them  into  a  system  ?  It  is  the  relation  of  inclusion  or 
exclusion,  as  the  case  may  be,  between  their  denota- 
tions. Applying  Euler's  circles  to  the  above  syllogism, 
we  have — 


Fig.  9. 

Aristotle's  idea  comes  out  clearly  enough  in  the  so- 
called  '  Dictum  de  omni  et  nullo '  (statement  concern- 
ing all  and  none)  which  is  called  the  *  Axiom  of  the 
Syllogism.'  "  Whatever  is  predicated  of  All  or  None  of 
a  term  is  predicated  of  whatever  is  contained  in  that 
term."  On  the  denotative  side,  this  axiom  is  suffi- 
ciently expressed  as  follows :  "  A  part  of  a  part  is  a  part 
of  the  whole."  Thus,  '  all  men  '  is  a  part  of  '  mortals ' 
and  '  Socrates  '  is  a  part  of  '  all  men.'  This  is  as  much 
of  an  axiom  as  the  corresponding  one  of  geometry. 

The  Elements  of  the  Syllogism.  We  noted  that 
Aristotle  thought  of  the  syllogism  as  a  means  of  estab- 
lishing a  relation,  negative  or  positive,  between  two 
terms  by  reason  of  their  relation  to  a  common  third 
term.  This  common  third  term  necessarily  appears  in 
each  of  the  premises,  but  does  not  appear  in  the  con- 
clusion. The  elements  of  the  syllogism  are,  therefore, 
three  terms  and  three  propositions.  The  term  common 
to  the  first  two  propositions  is  called  the  '  middle  term,' 
and  these  propositions  are  the  *  premises.'  The  conclud- 


THE  SYLLOGISM  AS  A  MECHANISM        111 

ing  proposition  is  the '  conclusion.'  The  other  two  terms, 
which  appear  in  the  conclusion,  are  the  '  extremes.' 
The  subject  of  the  conclusion,  is  called  the  'minor 
term,'  while  its  predicate  is  the  '  major  term.'  These 
are  the  extremes  mediated  by  the  middle  term.  The 
premise  which  contains  the  major  term  is  the  major 
premise  and  is  usually  stated  first ;  while  the  premise 
which  contains  the  minor  term  is  the  minor  premise. 

The  conclusion  is  the  moot  point,  the  problem  or  the- 
sis in  dispute.  It  is  from  it,  therefore,  that  our  thought 
starts.  This  fact  shows  that  we  are  concerned  in  the 
syllogism  with  the  mechanism  of  proof  rather  than  with 
a  movement  of  discovery.  The  question  before  our 
minds  is,  What  premises  will  justify  the  conclusion  ? 
We  are  seeking  the  grounds  of  the  conclusion.  At  this 
point  we  must  note  a  certain  difference  in  language 
form  according  as  our  thought  moves  downward  to  the 
conclusion  from  the  premises  or  backward  to  the  prem- 
ises from  the  conclusion.  In  the  first  case,  we  use  such 
terms  as  '  therefore,'  '  hence,'  etc. ;  in  the  second  case, 
such  terms  as  '  because '  and  '  since.' 

The  major  premise  is,  characteristically,  the  state- 
ment of  some  broad  general  principle,  some  generaliza- 
tion from  experience  which  can  be  applied  to  particular 
instances.  It  serves  both  to  interpret  and  support  the 
conclusion.  The  minor  premise,  on  the  other  hand, 
points  to  the  specific  application  which  is  in  question. 
It  is,  characteristically,  more  factual  than  the  major 
premise. 

The  Rules  of  the  Syllogism.  Having  once  com- 
prehended the  mechanism  of  the  syllogism  and  related 
it  to  the  logical  treatment  of  propositions  as  relations 


IW  THE  ESSENTIALS  OF  LOGIC 

of  exclusion  and  inclusion  between  classes,  it  is  easy  to 
formulate  and  to  prove  certain  rules  which  no  valid 
syllogism,  can  violate.  They  are  as  follows :  — 

1.  In  every  syllogism  there  should  be  three,  and  not 
more  than  three,  terms,  and  these  terms  must  be  used 
throughout  in  the  same  sense. 

2.  The  middle  term  must  be  distributed  at  least 
once  in  the  premises. 

3.  No  term  ought  to  be  distributed  in  the  conclusion 
that  was  not  distributed  in  the  premises. 

4.  No  conclusion  can  be  drawn  from  two  negative 
premises. 

6.  If  one  premise  is  negative,  the  conclusion  must 
be  negative. 

6.  No  conclusion  can  be  drawn  from  two  particular 
propositions. 

7.  If  one  premise  is  particular,  the  conclusion  must 
be  particular. 

The  first  rule  follows  from  the  mechanism  of  the 
syllogism.  It  is  founded,  as  we  saw,  on  the  recognition 
of  a  relation  between  the  major  and  minor  terms  be- 
cause of  their  relation  to  a  middle,  or  standard,  term. 
The  violation  of  this  rule  gives  rise  to  the  '  Fallacy  of 
Four  Terms.'  If  the  four  terms  were  clearly  distin- 
guishable, no  one  would  try  to  syllogize  them  together. 
Thus,  it  would  obviously  be  absurd  to  seek  to  draw  a 
conclusion  from  such  disparate  propositions  as,  'All 
men  are  mortal,'  and  '  Politics  are  improving  in  the 
United  States.'  But  it  sometimes  happens  that  a  term 
is  ambiguous,  there  seem  to  be  three  when  there  are 
actually  four  terms, 
j^  The  second  rule  brings  out  the  condition  without 


THE  SYLLOGISM  AS  A  MECHANISM       113 

which  the  middle  term  cannot  perform  its  assigned 
function.  Were  both  the  major  and  the  minor  terms 
related  to  only  a  part  of  the  middle  term,  we  could 


Fig.  10. 

have  no  assurance  that  they  were  related  to  the  same 
part.  In  other  words,  the  information  given  would  not 
tell  us  about  the  relative  position  of  the  terms  to  ap- 
pear in  the  conclusion.  This  indefiniteness  reveals  itself 
in  the  relations  of  the  circles  representing  the  three 
terms.  If  in  accordance  with  tradition,  we  let  S,  P^ 
and  M  stand  for  minor,  major,  and  middle  term  respec- 
tively, an  undistributed  middle  shows  itself  in  the  exist- 
ence of  different  possibilities.    (Fig.  10.) 

This  is  illustrated  more  concretely  in  the  following 
argument :  — 

All  voters  are  citizens; 
These  men  are  citizens; 
Therefore  these  men  are  voters. 

Diagrammatically,  this  syllogism  is  unsettled.  We 
are  not  able  to  determine  a  fixed  relative  position  for 
the  two  classes,  these  men  and  voters.    (Fig.  11.) 

A  breach  of  this  second  rule  involves  the  fallacy 
known  as  *  Undistributed  Middle.' 


114  THE  ESSENTIALS  OF  LOGIC 

The  basis  for  the  third  rule  is  the  very  nature  of  the 
conclusion  as  a  logical  sequence  from  the  premises.  We 
have  no  right  to  say  more  about  a  term  in  the  conclu- 
sion than  was  said  in  its  premise.  This  principle  has 
already  appeared  in  '  Immediate  Inference '  in  conver- 
sion. A  violation  of  the  third  rule  in  connection 
with  the  major  term  is  called  '  Illicit  Process  of  the 
Major,'  or,  more  briefly,  '  illicit  major ' ;  its  violation 
in  connection  with  the  minor  term,  '  Illicit  Process  of 
the  Minor,'  or  'illicit  minor.'    One  example  may  serve 

for  both. 

All  good  citizens  are  voters; 
This  person  is  not  a  good  citizen; 
Therefore  this  person  is  not  a  voter. 

The  conclusion  is  a  singular  proposition  and  nega- 
tive. It  will  be  remembered  that  the  predicate  of  a 
negative  proposition  is  distrib- 
uted. But  this  term  is  not  dis- 
tributed in  the  major  premise. 
Hence  this  is  a  case  of  illicit 
major.  This  fallacy  may  be  il- 
lustrated by  circles. 

The  fourth  rule  is  understood 
as  soon  as  we  realize  that  two 
■^•^*'  negative    premises    mean    that 

there  is  no  term  by  means  of  which  we  can  locate  the 
major  and  minor  with  reference  to  each  other.  Func- 
tionally, there  is  no  middle,  or  mediating,  term.  We 
know  that  >S'  and  P  both  fall  outside  of  M^  but  that 
fact  gives  us  no  clue  in  regard  to  their  interrelation. 
This  lack  of  mediation  appears  in  the  following  argu- 
ment :  — 


THE  SYLLOGISM  AS  A  MECHANISM       115 

No  bird  is  a  bat; 
This  is  not  a  bird; 
Therefore  this  is  a  bat. 

The  use  of  circles  may  make  the  situation  clearer. 


Bats 


Fig.  12. 

What  the  rule  points  to  is  our  inability  to  draw  a 
conclusion  from  the  information  given  in  the  premises. 
This  may  be  a  bat,  but  there  are  other  possibilities. 
In  applying  this  rule,  we  must  be  on  our  guard  against 
propositions  which  are  only  apparently  negative.  Care 
in  the  analysis  of  sentences  must  precede  the  use  of 
these  formal  rules. 

The  fifth  rule  is  seen  to  hold  as  soon  as  we  note  that 
the  two  terms  related  in  the  conclusion  do  not  have  the 
same  relation  to  the  middle  term.  If  one  premise  is 
negative,  one  of  the  extremes  must  be  excluded  in 
whole  or  in  part  from  the  middle  term.  But  the  other 
premise  must  be  affirmative  by  rule  four,  and  therefore 
asserts  a  partial  or  total  inclusion  in  the  middle  terra. 
This  alliance  with  a  term  which  excludes  the  other  ex- 
treme involves  it  also  as  a  party  to  the  exclusion. 

The  sixth  rule  can  be  demonstrated  by  means  of  the 
preceding  rules.  Both  premises  cannot  be  particular 
and  contain  the  necessary  distribution.  In  the  first 
place,  only  one  of  the  two  particulars  can  be  negative 
(rule  4).  There  are  left  three  possibilities,  //,  /  O, 
and  01.    II  fails  because  it  does  not  distribute  the 


116  THE  ESSENTIALS  OF  LOGIC 

middle  term.  /  0  and  O  /  fail  for  another  reason ; 
they  involve  a  negative  conclusion  (rule  5).  But  a 
negative  conclusion  means  that  the  major*  term  must 
be  distributed  in  the  major  premise.  But  neither  O  I 
nor  /  O  can  distribute  more  than  one  term.  Hence 
an  argument  having  two  particular  premises  is  invalid 
because  it  commits  either  the  fallacy  of  undistributed 
middle  or  that  of  illicit  major. 

The  seventh  and  last  rule  can  be  demonstrated  in 
much  the  same  way  as  the  sixth.  If  one  premise  be 
particular,  there  are  three  general  possibilities,  a  com- 
bination of  A  and  /,  of  A  and  O,  and  of  E  and  /.  If 
A  and  /  have  a  universal  conclusion,  the  minor  terra, 
the  subject  of  the  conclusion,  must  be  distributed  in  the 
minor  premise  to  avoid  an  illicit  minor.  But  the  pre- 
mises together  distribute  only  one  term,  and  this  must 
be  the  middle  (rule  2).  Bearing  in  mind  the  distri- 
bution of  the  terms  in  the  four  kinds  of  propositions, 
the  student  can  easily  prove  why  A  O  and  E  I  cannot 
have  universal  conclusions. 

The  Formal  Syllogism  and  Actual  Reasoning. 
In  the  present  chapter,  we  have  treated  the  syllogism 
as  a  mechanism  for  testing  the  consistency  of  an  argu- 
ment. While  such  knowledge  as  we  have  gained  is 
useful,  there  are  vital  objections  to  this  purely  formal 
view.  In  the  first  place,  if  the  major  premise  is  known 
to  be  true,  the  instance  subsumed  must  already  be 
known.  We  cannot  know  that  all  men  are  mortal 
without  feeling  that  Socrates  is  mortal.  There  is  no 
real  advance  in  thought  from  the  major  through  the 
minor  to  the  conclusion.  To  this  criticism  of  the  syl- 
logism, it  is  usually  replied  that  the  major  premise  is 


THE  SYLLOGISM  AS  A  MECHANISM       117 

really  the  statement  of  a  rule  which  we  take  to  be  with- 
out exceptions^  and  the  minor  is  the  statement  of  an 
instance.  If  so,  there  is  always  a  hazard  in  the  syllo- 
gism, a  point  which  we  shall  understand  better  when 
we  come  to  the  actual  movement  of  scientific  thinking. 
Another  objection  to  the  syllogism  concerns  the  middle 
term.  In  an  actual  argument,  how  can  you  be  certain 
that  you  have  an  unambiguous  middle  term  ?  Take  the 
following  example :  — 

All  men  love  good  stories; 
Smith  is  a  man; 
Therefore  Smith  loves  this  good  story. 

"  Smith  is  in  general  a  '  man,'  and,  therefore,  loves 
good  stories,  but  he  is  no  i  a  *  man '  for  the  purpose  of 
this  particular  conclusion ;  and  so  the  sense  of  '  man  ' 
in  the  two  premises  is  not  the  same,  and  this  vitiates 
the  argument."  ^  This  example  brings  out  the  fact  that 
it  is  not  always  easy  to  apply  a  rule  or,  conversely,  to 
know  when  an  instance  comes  under  a  rule.  Differ- 
ences may  be  very  important. 

In  actual  reasoning,  induction  and  deduction  march 
together.  Our  knowledge  of  general  principles  develops 
as  we  apply  them.  There  is  an  interpretation  of  rules 
by  new  facts  and,  at  the  same  time,  a  reading  of  facts 
in  terms  of  rules. 


REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  vni. 
Jones,  Logic,  Inductive  and  Deductive,  chap.  vni. 
Minto,  Logic,  Inductive  and  Deductive,  part  iv,  chap.  I. 
Schiller,  Formal  Logic,  chap.  xvi. 

1  Schiller,  Formal  Logic,  p.  200. 


CHAPTER  XI 

THE  FIGURES  AND  MOODS  OF  THE  SYLLOGISM 

The  Figures  of  the  Syllogism.  The  '  figure  '  of  a 
syllogism  is  determined  by  the  position  of  the  middle 
term.  Since  the  middle  term  may  be  subject  or  predi- 
cate in  each  of  the  two  premises,  four  arrangements  or 
figures  are  possible.  Using  the  conventional  symbols, 
we  may  state  these  four  figures  as  follows :  — 

1.  Mia  P  2.  PiaM  3.  M is  P  4.  P  is  i»f 

SiaM  SisM  M  ia  S.  Mia  S 

S  ia  P  SiaP  S  ia  P  -  S  ia  P 

Inspecting  these  arrangements  of  the  three  terms  in 
the  two  premises,  we  find  that  the  middle  term  is  the 
subject  of  the  major  premise  and  the  predicate  of  the 
minor  in  the  first  figure.  This  figure  was  considered  by 
Aristotle  the  most  satisfactory  and  was  therefore  called 
the  perfect  figure.  The  middle  term  is  contained  in  the 
major,  and  the  minor  in  the  middle  term. 

In  the  second  figure,  the  middle  term  is  the  predicate 
of  both  premises. 

In  the  third  figure,  it  is  the  subject  of  both  predi- 
cates. 

In  the  fourth  figure,  it  is  the  predicate  of  the  major 
premise  and  the  subject  of  the  minor  premise. 

The  Moods  of  the  Syllogism.  The  *  mood '  of  a 
syllogism  depends  upon  the  quality  and  quantity  of  the 
propositions  composing  it.  It  will  be  remembered  that 
there  are  four  kinds  of  propositions  symbolized  by  the 


FIGURES  AND  MOODS  OF  THE  SYLLOGISM    119 

letters  A^  E^  /,  and  0.  If  we  leave  out  all  question  of 
validity,  these  letters  may  be  combined  in  threes  to 
make  the  possible  moods  of  the  syllogism.  The  sixty- 
four  possible  moods  thus  obtained  are  as  follows :  — 

AAA  Ar&A  A-trAr  A-O^A  EAA  EEA  EIA  B-O^ 

AAE  AEE  AXE  AOE  EAE  EEE  E  I  E  EOE 

AAI  AE  I  A  I  I  AO  I  EA  I  **4  fe4-4-  EO  I 

AAO  AEG  A  I  O  AGO  EAG  EEG  EI  G  EGG- 

J^A^  4^^  i-^Ar  IGA  OAA  GEA  GIA  GGA 

I  AE  i-E^E-  I  I  E  I  GE  GAE  GEE  G  IE  GGE' 

I A  I  «B+  t^-t  t^-^  -e^A^-  GE  I  G  I  I  GG  I 

^t^tG-  (I  EG)  -f-i-e-  i-e^  GAG  GEG  GIG  GGG 

Fig.  IS. 

Many  of  these  mathematically  possible  moods  are  soon 
seen  to  be  invalid.  Thus,  by  applying  rules  4  and  5, 
that  no  conclusion  can  be  drawn  from  two  negative  or 
two  particular  premises,  we  can  decide  on  the  invalidity 
of  those  moods  through  which  a  line  is  drawn.  I E  O 
must  also  be  discarded  because  it  sins  against  rule  3  ; 
it  is  clearly  a  case  of  illicit  major.  We  are  left  with 
eleven  moods,  some  of  which  are  valid  in  certain  of  the 
four  figures  and  invalid  in  others.  The  reason  for  this 
variation  in  validity  according  to  figure  is  the  relation 
between  distribution  and  the  position  of  the  terms.  We 
must  now  ask  ourselves  what  moods  are  valid  in  the 
first,  second,  third,  and  fourth  figures  respectively. 

There  are  two  ways  of  determining  the  valid  moods 
of  each  figure :  by  inspection  and  by  the  establishment 
of  special  rules  for  each  figure.  We  shall  use  both 
methods  for  the  first  figure  and  then  only  state  the 


ISO 


THE  ESSENTIALS  OF  LOGIC 


special  rules  for  the  other  figures,  leaving  it  to  the 
student  to  demonstrate  them. 

Taking  the  eleven  moods  which  were  left  us  after  the 
first  general  elimination  and  arranging  the  terms  in 
accordance  with  the  first  figure,  we  have  the  following 
results : — 


A.  Ail  Mia  P 
A.  All  iSTis  M 
A.  AUSiaP 


A.  AU  3f  is  P 

A.  All  S  is  3f 
I.  Some  5  is  P 


-d.  X^  itf  is^ 
E.  No\<isi»f , 
E.  'mSm^ 


A.  AUJfisP 
J.  Some  Sis  Mi 
I.  Some  S  is  P 

E.  NoJlfisP 
J.  Some  S  is  Jlf 
0.  Some  S  is  not  P 

A.  "AilM  is. 
E.  No  fiP&J' 
0.  $<mie  iS  is  nt 


A.  All  M  isJP  E.  No  Jf  is  P 

O.  Somp>^s  not  P      A.  All  S  is  Jf.' 
0.  5<5me  S  ishQt  P       .B.  No  5  is  P 


E.  No  Mis  P 

A.  All  S  is  M" 

O.  Some  S  is  not  P 
Fig.  14. 


Applying  to  these  possible  moods  of  the  first  figure 
the  general  rules  of  the  syllogism,  we  soon  discover  that 
A  EE,  AE  0,  A  O  O,  /^  /,  and  O  ^  O  are  in- 
valid  because  of  an  undistributed  middle  or  an  illicit 
major.  Crossing  these  out,  we  have  A  A  A,^  A  A  I, 
All,  EAE,  EA  O,  and  EI  O  left  as  valid.  Of 
these  A  A  I  and  E  A  O  are  the  same  as  ^  -4  ^  and 
JE'  ^  ^  in  the  premises  and  have  weakened  conclusions ; 
they  have  therefore  no  essential  independent  value. 


FIGURES  AND  MOODS  OF  THE  SYLLOGISM   121 

This  analysis  of  the  possible  moods  of  the  first  figure 
should  illustrate  the  use  made  of  distribution  in  the 
syllogism.  An  inspection  of  the  valid  moods  leads  to  the 
discovery  of  the  two  following  special  rules  for  the  first 
figure :  — 

1.  The  minor  premise  must  be  affirmative.  /V 

2.  The  major  premise  must  be  universal. 
These  two  rules  can  also  be  demonstrated  by  means 

of  the  general  rules  of  the  syllogism.  To  prove  that  the 
minor  premise  must  be  affirmative,  we  use  the  indirect 
method  of  approach.  Suppose  it  to  be  negative ;  then 
the  conclusion  must  be  negative  (rule  5).  But  if  the 
conclusion  is  negative,  the  major  term  must  be  dis- 
tributed (rule  3).  To  distribute  P^  the  major  premise 
must  be  negative  since  only  the  predicates  of  negative 
propositions  are  distributed.  But  by  hypothesis,  the 
minor  premise  is  already  negative.  Hence  we  should 
have  two  negative  premises,  which  is  impossible.  It  fol- 
lows that  the  minor  premise  must  be  affirmative. 

Having  established  this  rule,  we  can  easily  show  that 
the  major  premise  must  be  universal.  An  affirmative 
minor  does  not  distribute  the  middle  term  in  the  first 
figure.  Hence  it  must  be  distributed  in  the  major  prem- 
ise (rule  2).  But  only  a  universal  will  do  this.  Thus 
the  second  special  rule  follows. 

A  similar  method  is  applicable  to  the  three  other 
figures.  For  the  sake  of  completeness,  the  special  rules 
for  these  figures  will  be  giv6n.  There  is  no  need  to  bur- 
den the  memory  with  them,  however,  as  in  actual  prac- 
tice the  general  rules  will  be  found  sufficient  as  tests  of 
validity. 

The  rules  for  the  second  figure  are :  — 


122  THE  ESSENTIALS  OF  LOGIC 

1.  The  conclusion  must  be  negative,  and  one  premise 
must,  also,  be  negative. 
1  '2.  The  major  premise  must  be  universaL 

For  the  third  figure  they  are  :  — 

1.  The  conclusion  must  be  particular. 

2.  The  minor  premise  must  be  affirmative. 

For  the  fourth  they  are  as  follows :  — 

1.  If  either  premise  be  negative,  the  major  premise 
must  be  universal. 

2.  If  the  major  premise  be  affirmative,  the  minor 
must  be  universal. 

8.  If  the  minor  premise  be  affirmative,  the  conclu- 
sion must  be  particular. 

Reduction  to  thie  First  Figure.  We  noted  that 
Aristotle  regarded  the  first  as  the  perfect  figure.  He 
did  so  because  the  Axiom  of  the  Syllogism  has  in  it 
its  simplest  application.  On  the  propositional  side,  the 
minor  premise  is  subsumed  under  the  major,  which  is  a 
universal.  The  process  of  changing  the  other  figures  to 
the  valid  moods  of  the  first  is  called  '  reduction.'  Dur- 
ing the  Middle  Ages,  when  the  syllogism  held  such  a 
revered  place,  elaborate  rules  for  this  reduction  were 
worked  out  and  embodied  in  mnemonic  lines.  This  pro- 
cess and  these  lines  have  had  such  a  place  in  history 
that  it  would  seem  unwise  not  to  mention  them.  There 
is  an  inimitable  flavor  of  the  past  about  them.  Reduc- 
tion is,  moreover,  a  process  which  casts  light  upon  the 
mechanism  of  the  syllogism  and  connects  it  with  con- 
version. 

The  following  verses  in  scholastic  Latin  served  the 


rtft 


FIGURES  AND  MOODS  OF  THE  SYLLOGISM    123 

double  function  of  recalling  the  valid  moods  of  each 
figure  and  of  giving  rules  for  reduction :  — 

Barbara,  Celarent,  Dani,  Femque  prioris  ; 
Cesare,  Camestres,  Festino,  Baroko,  secundsB  ; 
Tertia,  Darapti,  Disamis,  Datisis,  Felapton, 
Bokardo,  Ferison,  habet;  quarta  insuper  addit 
Bramantip,  Camenes,  Dimaris,  Fesapo,  Fresison. 

Unless  one  has  a  very  facile  memory,  there  is  not 
sufficient  value  in  the  stanza  to  justify  memorizing.  It 
is  interesting  to  see  its  construction  and  to  realize  how 
it  was  used.  The  vowels  in  the  names  give  the  moods. 
Thus, '  Barbara '  is  the  AAA  mood  of  the  first  figure. 
The  words  in  genuine  Latin  indicate  the  figures.  Sup- 
pose we  select  '  Disamis '  in  the  third  line.  Since  it  is 
in  the  third  figure  we  must  write  it  in  logical  symbols 
as  follows :  — 

/.  Some  Mis  P. 

A.  All  M  is  S. 

I.  Therefore  some  S  is  P. 

The  first  letter  of  each  mood  of  the  '  imperfect '  fig- 
ures indicates  the  corresponding  valid  mood  of  the  first 
figure  to  which  it  can  be  reduced.  Thus,  '  Cesare'  and 
'  Camestres '  of  the  second  figure  are  reducible  to 
*  Celarent '  of  the  first.  The  letters  s,  m,  and  p  also  have 
their  meaning  for  the  process  of  reduction.  Placed  after 
a  vowel,  s  indicates  that  the  proposition  represented  by 
the  vowel  must  be  converted  simply ;  m  (muta)  indicates 
that  the  premises  must  be  interchanged ;  whila^  shows 
that  the  proposition  after  which  it  is  placed  must  be  con- 
verted by  limitation,  or  per  accidens.  An  example  of 
reduction  will  make  this  clearer.  Take  '  Disamis '  again. 
The  initial  letter  indicates  that  '  Daiii '  is  the  corre- 


124  THE  ESSENTIALS  OF  LOGIC 

spending  mood  of  the  first  figure.  I A  I  oi  the  third 
figure  becomes  A  1 1  oi  the  first  by  conversion  of  the 
major  premise,  interchange  of  the  premises,  and,  finally, 
conversion  of  the  conclusion  to  correspond  to  the  trans- 
formation of  the  major  term  into  a  minor. 

Comparative  Value  of  the  Figures.  While  the 
tradition  in  logic  has  favored  the  view  that  the  first 
figure  is  somehow  better  than  the  others,  a  closer  anal- 
ysis has  shown  that  they  are  independently  valid  and 
do  not  need  reduction.  They  are  independent  types. 
In  other  words,  the  Axiom  of  the  Syllogism  holds 
primarily  of  the  first  figure  and  does  not  apply  directly 
tO'the  others.  Different  classes  of  arguments  naturally 
fall  into  different  forms.  Thus,  arguments  involving  the 
subsumption  of  an  instance  under  a  general  principle 
take  the  first  figure  ;  while  those  drawing  negative  con- 
clusions from  the  absence  of  distinctive  signs  take  the 
second.  The  following  example  of  a  second-figure  syl- 
logism will  bring  out  this  difference :  — 

All  fever-stricken  patients  are  thirsty. 
This  patient  is  not  thirsty. 
He  is  not  fever-stricken.^ 

A  close  inspection  of  this  argument  reveals  the  realiza- 
tion that  if  thirstiness  is  taken  as  a  sign  of  fever,  its 
absence  is  necessarily  a  sign  of  the  lack  of  fever.  It  is 
for  this  reason  that  Minto  speaks  of  the  second  as  the 
*  Figuref^f  Negative  Diagnosis.'  The  third  and  fourth 
figures  are  of  little  value.  It  should  be  remembered 
that  the  third  can  give  only  a  particular  conclusion. 
For   this   reason    it   has   sometimes   been   called  the 

1  Minto,  Logic. 


FIGURES  AND  MOODS  OF  THE  SYLLOGISM    125 

'Inductive  Figure.'  The  fourth  is  more  of  a  tmur  de 
force  and  is  not  always  admitted.  Arguments  do  not 
naturally  fall  into  it. 


REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  ix. 
Hibben,  Logic,  Deductive  and  Inductive,  part  i,  chap.  XVI. 
Jones,  Logic,  Inductive  and  Deductive,  chap.  tx. 
Minto,  Logic,  Inductive  and  Deductive,  bk.  i,  part  iv,  chaps,  n 
and  m. 


CHAPTER  XII 

ABBREVIATED  AND  EXPANDED  ARGUMENTS— EXTRA- 
SYLLOGISTIC  ARGUMENTS 

Enthymeme.  It  is  seldom  that  all  the  parts  of  an 
argument  are  stated  fully  and  explicitly.  Some  premise 
is  taken  for  granted  or  is  considered  too  obvious  to 
justify  formal  statement.  The  thinker  himself  has  not 
taken  the  time  to  analyze  and  formulate  the  grounds 
for  his  conclusion  or  he  feels  that  his  listeners  wish 
only  the  salient  points  and  can  supply  the  remainder. 
In  the  first  case,  what  he  says  reflects  what  has  been  up- 
permost in  his  mind ;  in  the  second  case,  he  wishes  to 
state  only  the  necessary  in  order  not  to  be  wooden  and 
pedantic.  All  this  is  natural  and  there  is  nothing  in  it 
which  the  logician  has  the  right  to  condemn.  Neverthe- 
less, such  condensation  has  its  dangers  against  which 
the  logician  must  issue  his  warning.  Oftentimes  sup- 
pressed premises  are  debatable  and  pass  just  because 
attention  has  not  been  called  to  them.  They  slink  by, 
as  it  were,  because  they  wear  caps  of  darkness  which 
hide  their  faces  from  scrutiny. 

The  logician  does  not  wish  to  be  the  enemy  of  wit, 
but  he  can  never  forget  that  he  is  the  guardian  of  rea- 
son. Brevity  is  the  soul  of  wit  and  of  the  epigram,  yet 
such  syncopation  must  be  capable  of  valid  enlarge- 
ment. It  is  of  the  character  of  such  enlargement  that 
the  syllogism  informs  us.  When  a  premise  or  the  con- 
clusion of  an  argument  is  not  stated,  the  argument 
has  the  form  of  an  enthymeme.  The  reasoning  is  not 


ABBREVIATED  ARGUMENTS  127 

fully  expressed.  An  enthymeme  is,  in  brief,  an  ellip- 
tical argument.  A  few  examples  will  make  this  clear :  — 

*  Death  cannot  be  an  evil,  being  universal.'  ^ 

*  He  is  in  love.  He  brushes  his  hat.'  ^ 

*  She  is  a  woman,  therefore  may  be  won.'  ^ 

Carlyle  says  of  Sansculottism :  *It  too  came  from 
God  ;  for  has  it  not  been  ? ' 

It  will  be  seen  from  these  examples  that  literature  is 
full  of  enthymemes.  They  add  to  the  charm  of  a  writer 
if  not  used  too  lavishly.  On  the  other  hand,  they  do 
not  have  so  assured  a  place  in  arguments  of  a  more  di- 
dactic character  as  in  science  and  philosophy.  Not  to 
leave  things  obscure  is  a  merit  in  these  fields. 

Enthymemes  are  of  the  first,  second,  or  third  order 
according  as  the  major  premise,  the  minor  premise,  or 
the  conclusion  is  wanting.  The  absence  of  the  conclu- 
sion is  a  rhetorical  device  t6  make  it  more  emphatic. 

It  is  usually  quite  easy  to  supply  the  missing  part 
of  the  argument.  The  two  propositions  which  are  given 
contain  the  three  terms.  Hence  all  that  is  needed  is 
the  perception  of  what  proposition  is  absent  and  its 
construction.  Thus  the  quotation  from  Goethe  given 
above  becomes  — 

Whatever  is  universal  is  not  an  evil; 
Death  is  universal ; 
Death  is  not  an  evil. 

Frosyllogisms  and  Episyllogisms.  Either  prem- 
ise of  a  syllogism  may  be  justified  by  making  it  the 
conclusion  of  another  syllogism.  When  this  is  done,  the 
result  is  a  complex  argument  in  which  one  syllogism 
prepares  the  way  for  a  second.  The  grounds  of  one  of 

1  Qoethe.         '  Much  Ado  About  Nothing.        ^  Titu$  Andronicus. 


Prosyllogpsm 


Episyllogism 


128  THE  ESSENTIALS  OF  LOGIC 

the  premises  of  the  final  conclusion  are  offered.  The  first 
syllogism  in  such  a  complex  is  called  the  '  prosyllogism/ 
and  the  last  the  'episyllogism.'  Any  connected  argu- 
ment of  length  involves  the  existence  of  interrelated 
syllogisms.  The  following  is  a  good  example :  — 

'Everything  which  is  able  to  restrain  trade  is  a 

source  of  danger ; 
Every  monopoly  is  able  to  restrain  trade ; 
Hence,  every  monopoly  is  a  source  of  danger. 
'  A  company  which  has  a  complete  control  of  a 

certain  commodity  is  a  monopoly  ; 
This  trust  has  complete  control  of  a  certain 

commodity  ; 
Hence,  this  trust  is  a  monopoly. 

Final  Conclusion.  This  trust  is  a  source  of  danger.^ 

It  wiU  be  noted  that  the  conclusions  of  the  first  two 
syllogisms  are  the  premises  of  the  final  conclusion. 

Sorites.  When  many  syllogisms  are  combined,  as 
above,  the  combination  is  called  a  '  polysyllogism.'  When 
all  the  intermediate  conclusions  are  suppressed,  a  poly- 
syllogism becomes  a  'sorites.'  A  sorites  is  a  chain  or, 
literally,  a  piling-up  of  premises  leading  to  a  conclusion. 
The  argument  gathers  weight  as  it  proceeds. 

Two  types  of  sorites  have  been  distinguished,  the 
*  Progressive '  or  '  Aristotelian,'  and  the  '  Regressive ' 
or  'Goclenian.'  The  Aristotelian  sorites  moves  from 
the  least  inclusive  term  to  the  most  inclusive,  from  the 
subject  of  the  conclusion  to  the  predicate. 

A  is  B.  All  Frenchmen  are  Europeans  ; 
B  is  C.  All  Europeans  are  men  ; 
C  is  Z).  All  men  are  animals  ; 
Z)  is  K.  All  animals  are  mortal  ; 

A  is  E.  All  Frenchmen  are  mortaL 

^1 

*  Jones,  Logic,  Inductive  and  Deductive. 


EXTRA-SYLLOGISTIC  ARGUMENTS         129 

The  Goclenian  sorites  moves  in  the  opposite  direc- 
tion. 

D  is  E.  All  animals  are  mortal ; 

C  is  D.  All  men  are  animals  ; 

B  is  C.  All  Europeans  are  men  ; 

A  is  B.  All  Frenchmen  are  Europeans ; 

Ais  E.  All  Frenchmen  are  mortal. 

A  sorites  can  be  expanded  into  a  polysyllogism  of 
which  each  unit  is  a  syllogism  of  the  first  figure.  In- 
spection will  show  the  student  that  the  order  of  each 
pair  of  premises  must  be  changed  to  accomplish  this  ex- 
pansion. 

The  following  example  of  the  use  of  the  sorites  in 
poetry  is  worth  quoting  to  show  how  a  logical  form  may 
be  clothed  upon  and  become  a  thing  of  beauty :  — 

The  longer  life  the  more  offence, 
The  more  offence  the  greater  paine, 
The  greater  paine  the  lesse  defence, 
The  less  defence  the  lesser  gaine  ; 
The  loss  of  gaine  long  yll  doth  trye, 
Wherefore  come  death  and  let  mee  dye. 

Come  gentle  Death,  the  ebbe  of  care, 
The  ebbe  of  care  the  flood  of  life, 
The  flood  of  life  the  joyf uU  fare, 
The  joyfull  fare  the  end  of  strife. 
The  end  of  strife  that  thing  wish  I ; 
Wherefore  come  death  and  let  mee  dye.* 

Eztra-Syllogistic  Arguments.  Not  all  forms  of 
reasoning  are  syllogistic  in  type.  For  example,  'J.  =5, 
B  =  C  .'.  A  =  C'  We  all  recognize  the  cogency  of  this 
reasoning,  yet  we  have  no  tendency  to  reduce  it  to  syl- 
logistic form.  Instead,  it  is  perceived  to  be  an  instance 
of  an  axiom  which  appeals  to  us  as  undeniable,  namely, 
1  Sir  Thomas  Wyatt,  1503-44. 


130  THE  ESSENTIALS  OF  LOGIC 

things  which  are  equal  to  the  same  thing  are  equal  to 
each  other.  The  argument  is  in  accord  with  the  axiom, 
yet  the  axiom  does  not  appear  as  a  major  premise  in  it. 
Deny  the  axiom,  and  you  would  be  forced  to  reject  the 
instance ;  but  it  is  possible  to  accept  the  instance  and 
seal  its  cogency  without  formulating  the  axiom.^ 

At  one  time  there  was  a  tendency  to  interpret  such  an 
argument  as  really  syllogistic,  as  an  enthymeme  with  an 
unformulated  major  premise,  and  to  complete  it  thus :  — 

Things  equal  to  the  same  thing  are  equal  to  each  other ; 
A  and  C  are  things  equal  to  the  same  thing  ; 
A  and  C  are  equal  to  each  other. 

But  inspection  shows  that  our  minor  premise  is  not 
an  exact  reproduction  of  the  original  argument,  which 
was  that  A  and  C  are  both  equal  to  B.  Even  with  this 
correction,  we  are  not  over  our  difficulties,  for  '  A  and 
C,'  the  apparent  minor  term,  is  not  a  term  at  all  but 
two  objects. 

The  truth  is,  that  the  syllogism  is  limited  to  the  re- 
lations between  classes  in  the  way  of  inclusion  and  ex- 
clusion. So  far  as  there  is  an  axiom  involved,  such  as 
the  dictum  de  omni  et  nullo.,  this  axiom  is  no  more  a 
major  premise  than  the  axiom,  that  things  equal  to  the 
same  thing  are  equal  to  each  other,  is  an  implied  ma- 
jor premise  for  the  mathematical  argument  referred  to 
above.  Deny  either  axiom,  and,  of  course,  the  particu- 
lar arguments  fall  to  the  ground.  An  examination  of 
other  types  of  arguments  may  make  the  situation  clearer 
and  enable  us  to  realize  that  in  the  syllogism  we  are 
dealing  with  a  comparatively  simple  sort  of  relation  be- 
tween classes.  The  point  is,  that  in  extra-syllogistic 
^  See  Joseph,  An  Introduction  to  Logic,  p.  273. 


EXTRA-SYLLOGISTIC  ARGUMENTS         131 

reasoning  we  have  to  do  with  different  systems  of  re- 
lation, some  of  which  are  definite  and  some  of  which 
are  indefinite.  Only  when  the  system  is  well  enough 
known  to  justify  a  conclusion  can  we  move  freely 
within  it. 

Quantitative  Relations 

A  is  greater  than  B) 

B  is  greater  than  C  \  Conclusion  valid 

A  is  greater  than  C] 

Relations  of  Direction 

A  is  north  of  B\ 

B  is  north  of  C  r  Conclusion  valid 

A  is  north  of  C] 

In  these  cases,  we  move  within  a  unitary  system  and 
can  travel,  as  it  were,  back  and  forth  in  it.  Each  sys- 
tem has  an  axiom,  but  the  axiom  is  founded  on  some- 
thing of  the  nature  of  immediate  perception.  In  the 
following  instance  the  absence  of  such  a  unitary  field 
of  relations  between  things  is  immediately  recognized :  — 

A  is  the  employer  of  B\ 

B  is  the  employer  of  C  r  Conclusion  invalid 

A  is  the  employer  of  C] 

The  study  of  extra-syllogistic  reasoning  is  valuable 
because  it  brings  into  relief  the  character  of  the  syllo- 
gism. It  enables  us  to  see  that  the  subject-matter 
is  fundamentally  important. 

REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  vi. 
Creighton,  A  n  Introductory  Logic,  chap.  X. 
Bradley,  The  Principles  of  Logic,  pp.  348-60. 
Joseph,  An  Introduction  to  Logic,  chaps,  xvi  and  xvn. 


CHAPTER  XIII 

HYPOTHETICAL  AND  DISJUNCTIVE  SYLLOGISMS 

In  a  very  real  sense  all  propositions  are  categorical, 
for  they  all  make  assertions.  But  it  has  been  customary 
for  logic  to  distinguish  propositions  in  which  a  predicate 
is  directly  asserted  of  a  subject  from  two  other  forms 
of  assertion,  the  hypothetical  and  the  disjunctive.  It  will 
be  remembered  that  these  propositional  forms  were 
briefly  defined  in  a  previous  chapter.  They  are  of 
interest  to  us  now  because  they  appear  as  the  major 
premises  of  two  other  kinds  of  syllogisms  called,  respec- 
tively, the  '  hypothetical '  and  the  '  disjunctive.' 

The  Hypothetical  Syllogism.  A  hypothetical 
proposition  combines  a  condition  with  a  consequent. 
'  If  this,  then  this,  is  the  general  form.  Thus,  '  If  it 
rains  this  afternoon,  I  shall  not  go  out  for  a  walk,'  and 
*  If  business  is  good,  I  shall  buy  an  auto,'  are  examples 
of  this  form  of  assertion  in  which  an  antecedent  is  re- 
lated to  an  inevitable  consequent.  A  little  reflection 
shows  how  extensive  is  this  expression  of  a  relation  be- 
tween two  events.  It  is  not  too  much  to  say  that  modern 
science  is  chiefly  concerned  with  the  discovery  of  rela- 
tions. In  practical  life,  again,  we  wish  to  know  what  to 
do  in  order  to  secure  certain  desirable  results.  If  we  can 
once  find  a  rule,  we  have  only  to  apply  it. 

In  a  hypothetical  syllogism,  the  major  premise  is 
hypothetical,  while  the  minor  is  categorical.  The  cate- 
gorical minor  either  affirms  the  antecedent  or  denies 


HYPOTHETICAL  SYLLOGISMS  133 

the  consequent  of  the  major  premise.  When  it  affirms 
the  antecedent,  the  syllogism  is  said  to  be  '  constructive,' 
or  in  the  modus  ponens  ;  when  it  denies  the  consequent, 
the  syllogism  is  '  destructive,'  or  in  the  modus  tollens. 
An  example  of  each  type  may  make  this  distinction 
clearer : — 

If  the  winter  is  really  over,  we  shall  have  some  warm  weather  ; 

The  winter  is  really  over  ; 

Therefore  we  shall  have  some  warm  weather. 

This  argument  is  constructive  because  we  affirm  the 
antecedent  and  thereby  have  the  right  to  affirm  the 
consequent  in  the  conclusion.  In  the  following,  how- 
ever, we  deny  the  consequent :  — 

If  human  life  were  considered  precious,  war  would  be  judged 
a  crime ; 
War  is  not  judged  a  crime  ; 
Therefore  human  life  is  not  considered  precious. 

It  should  be  noted  that  the  distinction  between  affirm- 
ative and  negative  has  no  meaning  for  hypothetical 
propositions.  We  are  either  able  to  affirm  a  connection 
between  an  antecedent  and  a  consequent  or  we  are  not 
able  so  to  do.  In  the  latter  case  we  are  not  able  to  pass 
any  judgment  of  this  character.  The  most  we  can  do  is 
to  state  a  probability.  In  a  later  chapter  we  shall  study 
the  nature  of  probability ;  but  it  would  complicate  things 
too  greatly  to  introduce  it  here. 

Another  point  needs  attention.  Either  the  anteced- 
ent or  the  consequent  or  both  may  be  negative.  In  such 
a  case  the  categorical  minor  may  be  negative  in  form  and 
yet  affirm  the  antecedent,  or  affirmative  in  form  and 
yet  deny  the  consequent.  The  way  to  avoid  error  is  to 
get  both  parts  of  the  major  premise  clearly  before  the 


184  THE  ESSENTIALS  OF  LOGIC 

mind,  and  then  to  see  them  in  their  relation  to  the  minor. 
In  the  following  syllogism  the  minor  is  negative  in  form, 
yet  it  affirms  the  antecedent :  — 

If  there  is  not  a  strike  at  the  works,  the  union  has  been  dis- 
rupted ; 

There  is  not  a  strike  at  the  works  ; 
Therefore  the  union  has  been  disrupted. 

The  Rule  of  the  Hypothetical  Syllogism.  The 

rule  of  the  hypothetical  syllogism  is  sometimes  spoken 
of  as  the  '  Law  of  Keason  and  Consequent.'  It  is  for- 
mulated thus:  The  truth  of  the  consequent  follows  from 
the  truth  of  the  antecedent,  and  the  falsehood  of  the  an- 
tecedent from  the  falsehood  of  the  consequent.  This  law 
expresses  the  nature  of  the  necessary  relation  affirmed 
to  exist  between  them. 

The  Fallacies  of  the  Hypothetical  Syllogism. 
To  attempt  to  draw  a  conclusion  by  denying  the  anteced- 
ent or  by  affirming  the  consequent  gives  rise  to  error. 
The  reason  for  this  is  apparent  so  soon  as  we  realize  that 
one  event  may  have  more  than  one  antecedent.  If  we 
have  information  that  tells  us  that  B  occurs  only  when 
A  occurs,  we  are  able  to  build  up  four  valid  hypotheti- 
cal syllogisms :  — 

If  A,  then  B  ;  Ah',  therefore  B  is. 

If  A,  then  B ;  A  is  not ;  therefore  B  is  not. 

If  A ,  then  B  ;  B  ia  ;  therefore  A  is. 

If  A,  then  B  j  B  ia  not  ;  therefore  A  is  not. 

In  such  a  case,  we  are  able  to  move  in  both  direc- 
tions because  B^s  existence  is  bound  up  only  with  A^s. 
But  ordinarily  this  is  not  the  case.  Hence  B  may  exist 
even  when  A  does  not.  An  example  may  make  this 
clearer :  — 


HYPOTHETICAL  SYLLOGISMS  135 

If  the  harbor  is  frozen,  the  ships  cannot  come  in  ; 
The  harbor  is  not  frozen ; 

Can  we  draw  a  conclusion  in  this  case  ?  No ;  because 
there  may  be  other  reasons  why  the  ships  cannot  come 
in.  The  harbor  may  be  mined,  or  there  may  be  a  storm. 

Reduction  to  Categorical  Form.  It  has  been 
customary  to  reduce  hypothetical  syllogisms  to  the  cate- 
gorical form  and  to  find  analogies  therein  for  these  two 
fallacies.  But  to  reduce  the  simple  to  the  complex  is 
wasted  effort,  and  there  is  little  doubt  that  much  of  our 
thinking  falls  naturally  into  the  hypothetical  form.  It 
would  seem  more  reasonable  to  reduce  categorical  syllo- 
gisms to  this  simpler  form.  For  the  sake  of  completeness, 
I  shall  perform  both  reductions. 

If  war  is  not  declared,  our  country  will  escape  disaster; 

But  war  will  not  be  declared; 

Therefore  our  country  will  escape  disaster. 

Reduced  to  categorical  form,  this  becomes:  — 

All  cases  of  war  not  being  declared  are  cases  of  our  conntry 
escaping  disaster; 
This  is  a  case  of  war  not  being  declared; 
Therefore  this  is  a  case  of  our  country  escaping  disaster. 

It  will  be  noted  that  a  relation  of  events  is  changed 
into  an  inclusion  of  classes.  As  a  matter  of  fact,  the 
major  premise  of  a  categorical  syllogism  usually  states 
a  principle,  and  the  minor  premise  an  instance.  Its 
meaning  is  often  more  clearly  expressed  as  a  hypo- 
thetical. 

All  men  are  mortal; 
Socrates  is  a  man ; 
Therefore  Socrates  is  mortal. 

really  means :  — 


1S6  THE  ESSENTIALS  OF  LOGIC 

If  man,  then  mortal; 
Socrates  is  a  man; 
Therefore  Socrates  is  mortal. 

*A11  men  are  mortal'  is  not  an  enuinerative  proposi- 
tion, but  the  statement  of  a  relation  between  man's 
nature  and  his  mortality.  If  it  were  enumerative,  we 
should  already  know  that  Socrates  was  mortal.  The 
logician  must  be  the  first  to  recognize  that  language 
forms  are  often  accidental. 

The  Disjunctive  Syllogism.  In  a  disjunctive  syl- 
logism, the  major  premise  is  disjunctive,  while  the 
minor  is  categorical.  Thus,  the  major  premise  expresses 
alternative  possibilities  among  which  the  minor  makes 
a  selection.  '  The  inventor  of  the  calculus  was  either 
Leibnitz  or  Newton,'  and  '  That  bird  was  either  a  sand 
martin  or  a  swallow,'  are  typical  disjunctives.  The 
minor  premise  either  asserts  or  denies  one  of  the  alter- 
natives. The  conclusion  either  denies  or  asserts  the 
other.  For  example  :  — 

This  man  is  either  very  clever  or  a  cheat; 
He  is  not  very  clever; 
Therefore  he  is  a  cheat. 

The  source  of  danger  is  in  the  major  premise.  The 
alternatives  there  offered  must  be  exclusive  of  each 
other.  Unless  this  is  the  case,  the  affirmation  of  one  of 
them  does  not  enable  us  to  make  an  assured  statement. 
Hence,  we  may  say  that  the  ideal  form  of  disjunction 
is  that  between  contradictories.  '  Sempronius  is  either 
honest  or  dishonest,'  '  This  man  acquired  his  wealth 
worthily  or  by  fraud,'  '  He  was  either  married  or  un- 
married '  are  examples  of  clear-cut  exclusion.  On  the 
other  hand,  a  man  may  be  both  a  knave  and  a  fool.  If 


DISJUNCTIVE  SYLLOGISMS  137 

so,  the  assertion  that  he  is  a  fool  does  not  enable  us  to 
proclaim  that  he  is  not  a  knave.  Again,  it  is  only  too 
common  to  assume  that  a  man  must  be  moved  either 
by  self-interest  or  by  altruism,  whereas  motives  are 
nearly  always  mixed.  Great  care  must  be  taken  in  for- 
mulating the  major  premise  of  a  disjunctive  syllogism. 

The  Dilemma.  A  dilemma  is  technically  defined 
as  an  argument  in  which  the  major  premise  is  a  com- 
plex hypothetical  proposition  and  the  minor  is  disjunc- 
tive. Practically,  it  means  the  presentation  of  two  or 
more  alternatives,  all  of  which  are  unpleasant. 

A  dilemma  may  be  constructive  or  destructive,  sim- 
ple or  complex.  If  the  antecedents  of  the  hypothetical 
major  are  affirmed  in  the  minor  premise,  the  dilemma 
is  said  to  be  '  constructive ' ;  if  the  consequents  are 
denied,  it  is  ♦  destructive.'  Thus  the  rule  at  work  is  the 
Law  of  Reason  and  Consequent.  The  new  element  is 
the  disjunctive  minor.  A  dilemma  is  simple  when  the 
consequents  are  the  same  for  both  antecedents ;  com- 
plex, when  the  consequents  of  the  hypothetical  major 
are  not  the  same  for  both  antecedents. 

The  following  is  an  example  of  a  simple  constructive 
dilemma :  — 

liAhsB,C\sD;  and  if  S  is  F,  C  is  D; 
But  either  A\s  B  ov  Eis  F; 
Therefore  C  ia  D. 

If  a  man  acts  in  accordance  with  his  own  judgment,  he  will  he 
criticized ;  and  if  he  is  guided  by  the  opinions  and  rules  of  others, 
he  will  be  criticized; 

But  he  must  either  act  in  accordance  with  his  own  judgment, 
or  be  guided  by  the  opinions  of  others ; 

Therefore,  in  any  case,  he  will  be  criticized.* 

*  Creighton,  An  Introductory  Logic. 


1S8  THE  ESSENTIALS  OF  LOGIC 

The  structure  of  the  complex  constructive  dilemma 
is  exemplified  in  this  argument :  — 

If  a  statesman  who  sees  his  former  opinions  to  be  wrong  does 
not  alter  his  course  he  is  guilty  of  deceit;  and  if  he  does  alter  his 
course  he  is  open  to  a  charge  of  inconsistency; 

But  either  he  does  not  alter  his  course  or  he  does; 

Therefore,  he  is  either  guilty  of  deceit,  or  he  is  open  to  a  charge 
of  incousistency. 

It  should  be  noted  that  the  conclusion  of  this  argu- 
ment is  disjunctive.  The  following  is  an  oft-quoted 
complex  destructive  dilemma :  — 

If  this  man  were  wise  he  would  not  speak  irreverently  of  the 
Scripture  in  jest;  and  if  he  were  good  he  would  not  do  it  in  ear- 
nest; 

But  he  does  it  either  in  jest  or  in  earnest; 

Therefore  he  is  either  not  wise  or  not  good. 

There  are  three  ways  of  meeting  a  dilemma,  all  of 
which  have  picturesque  names.  One  may  try  to  escape 
between  the  horns  of  a  dilemma,  these  being  the  alter- 
natives on  which  you  are  to  be  impaled.  To  escape  is 
to  show  that  there  is  some  other  alternative.  One  may 
try  to  rebut  a  dilemma  by  constructing  another  with  a 
contradictory  conclusion.  Or,  finally,  one  may  try  to 
take  a  dilemma  by  the  horns  by  accepting  an  alterna- 
tive and  proving  that  the  consequence  asserted  does  not 
follow. 

Since  it  is  difficult  to  get  an  exhaustive  disjunction 
for  the  minor  premise,  it  is  usually  easiest  to  escape 
between  the  horns.  The  rebuttal  of  a  dilemma  is  an  in- 
teresting process,  and  many  examples  have  come  down 
to  us  from  antiquity,  chief  of  which  is  the  story  of  Pro- 
tagoras and  Euathlus.  This  story,  called  Litigiosus^  is 
as  follows :  — 


DISJUNCTIVE  SYLLOGISMS  139 

Protagoras  had  agreed  with  Euathlus  to  teach  him 
rhetoric  for  a  fee,  of  which  half  was  to  be  paid  at  the 
conclusion  of  the  instruction,  and  the  remainder  when 
Euathlus  won  his  first  suit  in  court.  Observing  that 
the  latter  delayed  to  practice,  Protagoras  thought  he 
was  endeavoring  to  evade  payment,  and  therefore  him- 
self brought  a  suit  for  the  recovery  of  the  second  half 
of  his  fee.  He  then  argued  with  the  jury  that  Euathlus 
ought  to  pay  him,  in  the  following  way :  — 

If  Euathlus  loses  this  case,  he  ought  to  pay  by  the  judgment 
of  the  court;  and  if  he  wins  it,  he  ought  to  pay  by  his  own  agree- 
ment; 

But  he  must  either  lose  it  or  win  it; 

Therefore  he  ought  to  pay. 

Euathlus  rebutted  this  dilemma  by  a  counter-dilem- 
ma:— 

If  I  win  thb  case,  I  ought  not  to  pay  by  the  judgment  of  the 
court;  and  if  I  lose  it,  I  ought  not  to  pay  by  my  own  agreement; 
But  I  must  either  win  or  lose  it; 
Therefore  I  ought  not  to  pay. 

An  examination  of  these  two  dilemmas  shows  that 
each  antecedent  has  two  consequents,  one  only  of  which 
is  used  in  each  dilemma.  There  are,  in  other  words, 
two  standards  and  each  disputant  uses  them  only  when 
convenient.  This  conflict  of  standards  must  first  be  set- 
tled before  the  problem  can  be  cleared.  Has  Protagoras 
ground  for  action  ?  He  could  sue  him  only  for  refusing 
to  plead.  But  is  there  evidence  that  Euathlus  had 
agreed  to  become  a  pleader? 

The  dilemma  is  a  controversial  instrument.  When 
validly  constructed,  it  is  very  effective.  But  it  is  an 
instrument  which  may  be  turned  against  the  user  and 


140  THE  ESSENTIALS  OF  LOGIC 

then  becomes  a  trap  in  which  the  hunter  is  himself 
taken.  Before  resorting  to  the  dilemma,  one  should  be 
certain  that  the  situation  is  itseK  dilemmatic. 


REFERENCES 

Creighton,  An  Introductory  Logic,  chap.  XI. 
Bode,  An  Outline  of  Logic,  chap.  vii. 
Joseph,  An  Introduction  to  Logic,  chap.  xvi. 
Welton,  Manual  of  Logic,  vol.  i,  bk.  iv,  chap.  V. 


CHAPTER  XIV 

FALLACIES  IN  ARGUMENTATION 

What  a  Fallacy  is.  A  fallacy  is,  broadly  speak- 
ing, an  error  in  reasoning.  This  error  may  occur  at 
any  step.  We  may  misinterpret  our  perceptions,  or 
classify  things  wrongly,  or  work  out  bad  definitions,  or 
confuse  ideas,  or  draw  invalid  conclusions  from  prem- 
ises. The  risk  of  misjudgment  is  constantly  present. 
The  task  confrontmg  the  human  mind  is  twofold,  that 
of  attaining  knowledge  and  that  of  handling  it  properly 
after  it  has  been  attained ;  and  neither  part  of  this  task  is 
easy.  Mistakes  are  constantly  being  made.  But  since 
human  beings  must  think,  because  of  the  very  require- 
ments of  their  life,  the  best  they  can  do  is  to  examine 
every  stage  and  aspect  of  thinking  in  order  to  reduce 
mistakes  to  a  minimum.  It  was  this  need  which  gave 
rise  to  logic.  We  may  say,  then,  that  thinking  is  an 
adventure  and  that  fallacies  are  misadventures. 

A  Classification  of  Fallacies.  The  traditional 
classification  of  fallacies  is  into  '  deductive '  and  '  induc- 
tive '  fallacies.  We  shall  interpret  this  classification  as 
corresponding  to  the  twofold  task  referred  to  above. 
Man  must  correctly  handle  the  knowledge  he  already 
has,  both  in  his  private  thinking  and  in  his  arguments 
with  other  people ;  and  he  must  be  able  to  make  inves- 
tigations into  new  fields.  Where  errors  creep  into  one's 
own  thinking  or  into  argumentation,  although  no  es- 
sentially new  data  or  principles  are  involved,  we  have 


142  THE  ESSENTIALS  OF  LOGIC 

to  do  with  'deductive'  fallacies  or  fallacies  in  argu- 
mentation; where,  on  the  other  hand,  errors  arise  in 
attempts  to  extend  the  boundaries  of  knowledge,  they 
are  better  called  'inductive'  fallacies.  In  the  present 
chapter,  we  are  concerned  primarily  with  the  former. 

Classification  of  Deductive  Fallacies.  It  is  dif- 
ficult to  get  a  single  positive  principle  of  classification 
for  fallacies.  The  usual  division  is  into  '  formal '  and 
'material.'  Formal  fallacies  are  those  which  involve 
some  breach  of  the  logical  rulea  of  the  syllogism.  Since 
obversion  and  conversion  are  closely  connected  with  the 
syllogism,  false  conversion  and  false  obversion  may  be 
placed  here.  Material  fallacies  result  from  a  misappre- 
hension of  the  content  or  from  false  assumption. 

Formal  fallacies  have  been  treated  in  detail  in  con- 
nection with  the  chapters  devoted  to  the  syllogism.  I 
shall  run  over  the  list  and  suggest  that  the  student 
seek  to  clear  up  his  memory  in  regard  to  them.  They 
are  as  follows :  (1)  False  conversion  ;  (2)  False  ob- 
version ;  (3)  Four  Terms;  (4)  Undistributed  Mid- 
dle; (5)  Illicit  Major  ;  (6)  Illicit  Minor  ;  (7)  Two 
Negative  Premises  ;  (8)  Two  Particular  Premises ; 

(9)  Affirmative  Conclusion  with  Negative  Premise; 

(10)  Denying  the  Antecedent;  (11)  Affirming  the 
Consequent ;  (12)  Incomplete  Disjunction.  Of  these, 
special  stress  should  be  put  on  the  Undistributed  Mid- 
dle and  the  fallacy  of  Four  Terms.  All  verbal  fallacies 
appear  syllogistically  as  Four  Terms.  Whenever  the 
middle  term  is  vague  or  indefinite,  there  is  danger  of 
an  ambiguous  middle.  While  M  is  P,  yet  S  may  be 
Mwith  a  difference. 

Material  fallacies  fall  into  two  main  divisions,  those 


FALLACIES  IN  ARGUMENTATION  143 

connected  with  definition  and  those  involving  unwar- 
ranted assumption.  If  terms  are  not  clearly  defined, 
some  form  of  ambiguity  is  almost  sure  to  appear.  On 
the  other  hand,  the  logic  of  argumentation  demands 
that  the  conclusion  be  not  assumed  but  deduced  from 
accepted  premises.  The  following  classification  will 
serve  as  a  guide :  — 

Material  Fallacies 


Fallacies  of  Equivocation 

Fallacies  of  Unwarranted 
Assumption 

1.  Ambiguous  and  Shifting 
Terms. 

2.  Amphiboly. 

3.  Composition. 

4.  Division. 
6.  Accident. 
6.  Accent. 

1. 
2. 
3. 

Begging  the  Question. 
Complex  Question. 
Irrational  Evidence. 

(a)  Argumentum  ad  hominem. 

(b)  Argumentum  ad  populum. 

(c)  Argumentum  ad  ignoran- 
tiam. 

7.  Figure  of  Speech. 

(d)  Argumentum  ad  vericun- 
diam. 

4. 

Irrelevant  Conclusion. 

6. 

Non  sequitur. 

Fallacies  of  Equivocation.  1.  Words  may  be  in- 
definite and  yet  not  ambiguous.  When,  however,  there 
is  the  slightest  danger  of  misunderstanding,  words 
should  be  defined  or  else  clearly  qualified  by  the  con- 
text. In  literature,  the  suggestiveness  of  a  word  may 
depend  upon  its  capacity  to  awaken  many  lines  of  asso- 
ciation. But  precision  rather  than  suggestiveness  is  fun- 
damental for  reasoning.  Especially  is  this  the  case  in 
long  arguments  in  which  the  meaning  of  a  term  may 
shift  from  stage  to  stage  if  care  be  not  taken.  For  in- 
stance, an  argument  may  start  with  legal  right  and 
conclude  with  moral  right.    The  following  fallacious 


144  THE  ESSENTIALS  OF  LOGIC 

syllogism  may  serve  as  an  example  of  a  subtle  form  of 
equivocation  called  '  Ambiguous  Middle ' :  — 

All  able  men  are  consistent  with  themselves; 

He  who  changes  his  opinions  is  not  consistent  with  himself; 

He  who  changes  his  opinions  is  not  an  able  man. 

A  moment's  reflection  shows  that  the  reference  to 
time  is  different  in  the  two  premises. 

2.  When  the  ambiguity  lies  in  the  very  structure  of 
the  sentence,  the  resultant  fallacy  is  called  'Amphib- 
oly.' The  sentence  permits  of  a  double  interpretation. 
Such  cases  as  occur  to-day  are  accidental  and  have 
little  significance  except  as  a  warning  against  careless 
writing.  The  following  want-advertisements  are  good 
examples :  — 

Wanted:  a  groom  to  look  after  two  horses  of  a  pious  turn  of 
miud.^ 

A  second-hand  morris-chair  is  wanted  by  a  bachelor  with  richly 
carved  claw-feet. 

The  classical  cases  of  Amphiboly  are  the  decrees  of 
the  oracle  at  Delphi.  The  response  of  the  oracle  to 
Pyrrhus  is  an  excellent  instance :  "  Pyrrhus  the  Ro- 
mans can,  I  say,  subdue." 

3.  The  fallacy  of  Composition  arises  when  an  attri- 
bute is  predicated  of  a  whole,  which  holds  only  of  a 
part.  The  object  to  which  the  property  is  fallaciously 
assigned  is  usually  an  aggregate.  Thus,  to  argue  that 
a  country  is  prosperous  because  many  business  men 
are  making  money,  is  essentially  to  commit  the  fallacy 
of  Composition.  Very  similar  to  this  is  the  following 
argument :  — 

^  Gibson,  The  Problem  of  Logic. 


FALLACIES  IN  ARGUMENTATION  145 

The  manufacturers  of  woolens  are  benefited  by  the  duty  on 
woolen  goods;  the  manufacturers  of  cotton  by  the  duty  on  cotton; 
the  farmer  by  the  duties  on  wool  and  grain ;  and  so  on  for  all  the 
other  producing  classes;  therefore,  if  all  the  products  of  the 
country  were  protected  by  an  import  duty,  all  the  producing 
classes  would  be  benefited  thereby. 

It  will  be  noted  that  the  mind  easily  tends  to  pass 
from  individual  cases  and  classes  to  larger  wholes  with- 
out thought  of  the  new  influences  and  relations  which 
are  at  work  in  such  a  whole. 

4.  The  fallacy  of  Division  is  the  converse  of  Com- 
position. It  consists  in  the  assignment  to  the  part  of 
attributes  which  are  true  only  of  the  whole.  We  can 
bring  this  fallacy  into  touch  with  the  distinction  be- 
tween the  collective  and  the  distributive  use  of  terms 
by  saying  that  it  arises  from  a  disregard  of  these  two 
uses.  In  the  major  premise,  the  term  may  be  used  col- 
lectively, while  it  is  employed  distributively  in  the 
minor.  The  following  example  illustrates  this  hasty 
movement  from  the  whole  to  the  parts :  — 

He  cannot  be  innocent,  for  he  was  a  member  of  the  mob  which 
committed  the  deed. 

We  are  especially  liable  to  fall  into  this  error  in 
discussions  upon  social  and  political  topics.  Because 
people  act  rather  foolishly  or  selfishly  as  units  in  a 
group,  it  does  not  follow  that  their  conduct  will  be  of 
the  same  character  when  they  are  acting  as  individuals. 
As  one  writer  has  forcefully  put  it,  individual  morality 
has  outstripped  crowd  morality  by  many  centuries. 
"  Perhaps  the  commonest  form  of  the  fallacy  is  that 
which  it  takes  in  such  arguments  as,  '  It  must  be 
wrong  for  you  to  act  in  this  manner,  because  if  every 


146  THE  ESSENTIALS  OF  LOGIC 

one  did  so,  the  consequences  would  be  disastrous.'  We 
start  by  urging  that  if  A  and  B  and  C  .  .  .  (conjunc- 
tive} acted  in  some  specified  manner  —  the  welfare  of 
the  world  would  be  fatally  affected,  and  we  go  on  to 
argue  that  no  less  fatal  consequences  must  follow 
when  A  or  B  or  C  (disjimctive)  act  in  the  manner 
specified."  ^ 

5.  The  fallacy  of  Accident  consists  in  the  applica- 
tion of  an  abstract  principle  without  allowance  for 
qualifying  conditions.  Because  water  boils  at  212® 
Fahrenheit  and  such  water  will  boil  an  &g%  in  five 
minutes,  it  does  not  follow  that  boiling  water  on  the 
top  of  a  mountain  will  cook  an  egg  in  that  number  of 
minutes.  Because  charity  is  a  virtue,  we  must  not  con- 
clude that  it  is  necessarily  virtuous  to  give  a  beggar  a 
dollar.  It  may  do  him  more  harm  than  good.  Such  ab- 
stract principles  are  not  true  universals  and  the  mis- 
take lies  in  so  taking  them.  In  argument,  it  is  so  easy 
to  make  general  pronouncements  and  shove  to  one  side 
those  qualifications  which  a  keener  desire  for  truth 
would  take  accoimt  of.  "  There  is  no  fallacy  more  in- 
sidious than  that  of  treating  a  statement  which  for 
many  purposes  is  true  as  if  it  were  true  always  and  with- 
out qualification."  2 

The  converse  fallacy  of  Accident  consists  in  the  pas- 
sage from  what  is  true  under  certain  circumstances  to 
an  abstract  principle  based  upon  these  instances.  In- 
ductively, it  takes  the  form  of  a  hasty  generalization. 
An  individual  who  argued  that  a  college  education  was 

1  Gibson,  The  Problem  of  Logic,  p.  284.  Cf.  Welton,  Manual  of 
Logic,  vol.  II,  p.  247. 

"  Joseph,  An  Introduction  to  Logic,  p.  549. 


FALLACIES  IN  ARGUMENTATION  147 

valueless  because  Edison  and  Ford  did  not  have  one 
would  be  committing  this  fallacy.  The  type  of  argu- 
ment is,  I  think,  easily  recognized. 

Both  the  direct  and  the  converse  fallacies  of  J^cci- 
dent  are  important  because  they  bear  witness  to  a 
deep-seated  tendency  to  think  abstractly  and  dogmati- 
cally. Only  the  careful  thinker  does  justice  to  both 
principles  and  facts.  Lotze,  a  German  philosopher  of 
the  last  century,  wrote  the  following  very  sane  com- 
ment :  "  Two  general  modes  of  fallacious  thought  are 
developed  by  the  habitual  commission  of  these  fallacies, 
and  illustrate  them  on  a  grand  scale.  The  first  is  doc- 
trinairism,  the  second  narrow-mindedness.  The  doctri- 
naire is  an  idealist  who  refuses  to  see  that  though 
ideas  may  be  right  in  the  abstract,  yet  the  nature  of 
the  circumstances  under  which  and  of  the  objects  to 
which  they  are  to  be  applied,  must  limit  not  only 
their  practicality,  but  even  their  binding  force.  The 
narrow-minded,  on  the  other  hand,  can  recognize  and 
esteem  no  truth  and  no  ideal,  even  the  most  univer- 
sally valid,  except  in  that  special  form  to  which  they 
have  become  accustomed  within  a  limited  circle  of 
thought  and  personal  observation.  Life  is  a  school 
which  corrects  these  habits  of  mind.  The  parochially 
minded  man  sees  things  persist,  in  spite  of  himself,  in 
taking  shapes  which  he  considers  unprecedented,  but 
he  finds  the  world  somehow  survives  it,  and  learns  at 
last  that  a  system  of  life  may  be  excellent  and  precious, 
but  that  it  is  rash  from  that  to  argue  that  it  is  the  only 
proper  mode  of  orderly  existence.  And  the  enthusiast 
for  ideals,  when  he  sees  the  curtailment  which  every  at- 
tempt at  realization  inflicts  on  them,  learns  the  lesson 


148  THE  ESSENTIALS  OF  LOGIC 

which   the    disjunctive   theorem    might    have   taught 
him."i 

6.  The  fallacy  of  Accent  is  due  to  a  misleading 
emphasis.  When  words  are  taken  from  their  context, 
they  often  seem  to  have  a  meaning  which  an  investiga- 
tion shows  was  not  the  intent  of  the  author.  This  error 
is  near  enough  to  misinterpretation  caused  by  mis- 
placed emphasis  to  be  classified  with  it.  Another  in- 
stance is  the  use  of  italics  in  a  quotation  where  no 
words  were  originally  italicized.  Jevons  points  out  a 
laughable  case  of  the  use  of  italics  lending  itself  to 
misunderstanding.  In  the  First  Book  of  Kings,  Xiii,  27, 
the  translators  added  a  word  to  complete  the  sentence 
and  put  it  in  italics  to  indicate  this  fact.  The  result  was 
as  follows :  "  And  he  spake  to  his  sons,  saying,  Saddle 
me  an  ass.  And  they  saddled  Aim."  "  It  is  curious," 
continues  Jevons,  "  to  observe  how  many  and  various 
may  be  the  meanings  attributable  to  the  same  sentence 
according  as  emphasis  is  thrown  on  one  word  or  an- 
other. Thus  the .  sentence,  '  The  study  of  logic  is  not 
supposed  to  communicate  the  knowledge  of  many  use- 
ful facts,'  may  be  made  to  imply  that  the  study  of 
logic  does  communicate  such  a  knowledge,  although  it 
is  not  supposed  to  do  so ;  or  that  it  communicates  a 
knowledge  of  many  useless  facts."  ^ 

7.  The  fallacy  of  Figure  of  Speech  is  due  to  the 
ambiguous  character  of  some  verbal  inflection.  It  is  not 
of  much  importance  in  a  language  like  English  in  which 
inflection  is  at  a  minimum.  The  best  case,  and  the  one 
usually .  quoted  by  logicians,  is  found  in  Mill's  book, 
Utilitarianism.  He  is  trying  to  prove  that  pleasure  is 

*  Logic,  vol.  II,  p.  5  (Eng.  trans.).  ^  Lessons  in  Logic,  p.  175. 


FALLACIES  IN  ARGUMENTATION  149 

the  chief  good.  "  The  only  proof,"  he  writes,  "  capable 
of  being  given  that  an  object  is  visible  is  that  people 
actually  see  it.  The  only  proof  that  a  sound  is  audible  is 
that  people  hear  it :  and  so  of  the  other  sources  of  our 
experience.  In  like  manner,  I  apprehend,  the  sole  evi- 
dence it  is  possible  to  produce  that  anything  is  desirable, 
is  that  people  actually  desire  it."  But  '  visible '  and  '  au- 
dible '  mean  what  can  be  seen  and  heard,  while  '  desira- 
ble '  means  what  is  worth  desire  or  ought  to  he  desired. 
Mill  did  not  notice  the  change  in  meaning  because  he 
was  paying  too  strict  attention  to  the  form  of  the  words. 
A  similar  mistake  is  sometimes  made  when  the  original 
or  etymological  meaning  of  a  word  is  stressed  and  the 
more  usual  meaning  of  the  present  disregarded.  Thus, 
to  argue  that  representatives  must  passively  represent 
their  constituents  is  to  commit  this  fallacy. 

Fallacies  of  Un-warranted  Assumption.  These 
fallacies  consist  in  the  entrance  into  the  argument  of 
an  unwarranted  element  of  assumption.  Either  the 
point  at  issue  is  assumed  (Begging  the  Question,  and 
Complex  Question),  or  the  evidence  adduced  is  irrele- 
vant (Irrational  Evidence),  or  the  conclusion  is  beside 
the  point  (Irrelevant  Conclusion,  and  Non  Sequitur^. 
In  all  these  cases,  the  conclusion  is  not  demonstrated 
and  the  fallacy  consists  in  the  assumption  that  it  is. 

1.  Begging  the  Question^  or  JPetitio  Prindpii,  is 
the  assumption  of  the  point  to  be  proved.  In  an  argu- 
ment, it  consists  in  the  taking  for  granted  what  an  op- 
ponent would  not  admit  if  its  significance  were  under- 
stood ;  it  is  the  "  surreptitious  assumption  of  a  truth 
you  ai-e  pretending  to  prove." 

There  are  two  distinguishable   types  of   question- 


150  THE  ESSENTIALS  OF  LOGIC 

begging.  In  the  one,  the  conclusion  we  wish  to  prove 
is  directly  assumed  under  another  name ;  in  the  other, 
some  larger  general  principle  which  includes  the  point 
in  dispute  is  taken  for  granted. 

The  first  type  appears  either  as  a  question-begging 
epithet  or  as  reasoning  in  a  circle.  To  call  a  prisoner 
before  the  bar  a  worthless  good-for-nothing  whom  every 
one  has  suspected  for  a  long  time  is  not  to  prove  that 
he  has  committed  the  crime  of  which  he  is  accused,  but 
to  prejudice  the  jury  against  him.  Epithets  are  insidi- 
ous attempts  to  lead  the  minds  of  the  listeners  in  the 
desired  direction  independently  of  genuine  evidence. 
Nowhere  is  this  procedure  more  frequently  resorted  to 
than  in  politics.  Mud-slinging  is  the  bane  of  political 
life,  and,  unfortunately,  it  has  its  bad  ethical  effect. 
Those  who  drop  into  the  practice  must  lose  some  meas- 
ure of  their  intellectual  integrity.  Logic  has  its  morali- 
ties. Reasoning  in  a  circle  consists  in  the  use  of  a  prem- 
ise which  is  only  the  desired  conclusion  stated  in  other 
words.  It  is  difficult  to  offer  a  good  example  in  brief 
compass  of  this  species  of  Begging  the  Question,  since 
it  is  more  apt  to  occur  in  a  long  argument.  Often  argu- 
ments do  not  make  any  advance,  but  twist  and  turn  and 
repeat  the  same  things  in  different  words.  Absence  of 
a  clear-cut  argument  is  nearly  always  a  sign  of  an  ele- 
ment of  circular  thinking.  The  individual  tries  desper- 
ately to  make  an  advance,  but  really  turns  around  the 
same  fixed  ideas  with  much  noise  of  asseveration.  It  is 
a  form  of  logical  hemming  and  hawing.  When  there 
is  a  sophistic  element,  an  intent  to  deceive  and  to  se- 
cure victory  at  all  hazards,  reasoning  in  a  circle  becomes 
argument  in  a  circle.  A  frequently  used  device  in  Eng- 


FALLACIES  IN  ARGUMENTATION  151 

Ush  is  to  state  the  proposition  to  be  proved  in  words 
of  Saxon  origin  and  then  to  give  as  reason  for  it  the 
same  proposition  in  words  of  classical  origin.  The  fol- 
lowing example  from  Whately  is  much  quoted  in  this 
connection :  "  To  allow  every  man  an  unbounded  free- 
dom of  speech  must  always  be,  on  the  whole,  advanta- 
geous to  the  State,  for  it  is  highly  conducive  to  the 
interests  of  the  community  that  each  individual  should 
enjoy  a  liberty  perfectly  unlimited  of  expressing  his 
sentiments." 

The  second  general  type  of  question-begging  consists, 
as  we  have  said,  in  the  assumption  of  a  larger  principle 
than  the  one  in  dispute  from  which  this  latter  may  be 
deduced.  It  has  much  in  common  with  the  fallacy  of 
Accident.  Thus,  if  a  piece  of  legislation  concerning  a 
particular  remediable  wrong  were  under  discussion,  it 
would  be  question-begging  to  make  appeal  to  some 
abstract  principle,  like  '  AH  legislation  which  interferes 
with  the  right  of  free  contract  is  bad.'  At  one  time  — 
in  the  past,  I  am  thankful  to  say  —  certain  abstract 
principles  of  political  economy  were  used  in  this  way 
as  maxims  against  remedial  legislation ;  and  we  all  know 
how  both  the  conservative  and  the  demagogue  make 
use  of  slogans. 

In  regard  to  this  fallacy,  it  is  well  to  bear  in  mind 
what  De  Morgan  called  its  opponent  fallacy :  "  It  is 
the  habit  of  many  to  treat  an  advanced  proposition  as 
a  begging  of  the  question  the  moment  they  see  that,  if 
established,  it  would  establish  the  question."  Such  an 
attitude  is  not  playing  fair. 

2.  When  a  question  is  so  stated  as  to  involve  a  ques- 
tionable assumption,  it  is  called  a  'Complex  Question.' 


152  THE  ESSENTIALS  OF  LOGIC 

Any  direct  answer  to  such  a  question  implies  the  ad- 
mission of  the  point  assumed.  Complex  Question  may 
be  a  trick  as  in  the  following  examples :  '  Have  you  left 
off  beating  your  wife?'  'Has  the  practice  of  heavy 
drinking  ceased  in  your  part  of  the  country  ? '  Or  it 
may  be  due  to  the  fact  that  the  interrogator  has  not 
analyzed  all  that  his  question  involves.  A  teacher  in 
philosophy  may  be  asked  how  he  explains  telepathy. 

3.  "  The  characteristic  appeal  which  Science,  in  its 
processes  of  reasoning,  makes  to  the  mind  is  the  argu- 
mentum  ad  judicium^  or  appeal  to  reason.  When  the 
appeal  is  not  to  the  impartial  reason,  but  to  the  feelings, 
passions,  prejudices  of  men,  it  is,  from  the  logical  point 
of  view,  radically  irrelevant^  and  involves  the  fallacy  of 
Irrational  Evidence."^ 

This  fallacy  is  akin  to  the  first  type  of  Begging  the 
Question ;  the  difference  lies  in  the  openness  of  the  ap- 
peal to  the  non-logical.  Locke's  treatment  of  the  vari- 
ous forms  of  this  fallacy  is  classic.  "  Of  all  the  argu- 
ments," he  writes,  "  that  men  ordinarily  make  use  of, 
the  argument  ad  judicium  alone  brings  true  instruction 
with  it,  and  advances  us  in  the  way  to  knowledge.  .  .  . 
For  (1)  it  argues  not  another  man's  opinion  to  be  right, 
because  I,  out  of  respect,  or  any  other  consideration  but 
that  of  conviction,  will  not  contradict  him.  (2)  It  proves 
not  another  man  to  be  in  the  right  way,  nor  that  I  ought 
to  take  the  same  with  him,  because  I  know  not  a  better. 
(3)  Nor  does  it  follow  that  another  man  is  in  the  right 
way  because  he  has  shown  me  that  I  am  in  the  wrong."  ^ 
Putting  these  conclusions  into  touch  with  the  experience 

1  Gibson,  The  Problem  of  Logic,  p.  287. 

*  Locke,  Essay  concerning  Human  Understanding,  bk.  rv,  chap.  zvn. 


FALLACIES  IN  ARGUMENTATION  153 

that  any  appeal  to  feeling  must  be  regarded  with  sus- 
picion, logicians  have  distinguished  the  following  varie- 
ties of  Irrational  Evidence :  — 

(a)  Argumentum  ad  hominem.  In  this  fallacy  the 
argument  is  directed  against  the  character  of  the  man 
who  is  the  opponent  instead  of  adhering  to  its  proper 
task  of  proving  the  point  at  issue.  Too  often,  calumny 
and  gossip  are  resorted  to  in  order  to  make  out  a  case 
and  win  the  decision.  Here,  again,  logic  touches  upon 
ethics.  If  the  ideal  held  is  that  the  end  justifies  the 
means,  such  arguments  come  under  rhetoric  and  the 
only  point  of  attack  is  their  effectiveness.  They  are 
more  non-logical  than  illogical.  As  a  matter  of  fact, 
they  are  usually  employed  by  individuals  who  are  fully 
aware  of  what  they  are  doing.  They  are  the  tricks  of 
the  sophist.  A  story  is  told  of  O'Connell  that  on  one 
occasion,  when  he  had  to  defend  a  man  who  was  clearly 
in  the  wrong,  the  counsel  for  the  prosecution  was  a  cer- 
tain Mr.  Kiefe,  who  had  come  in  for  some  money  in 
rather  a  questionable  way,  and  had  taken  the  name  of 
O'Kiefe.  O'Connell  commenced  his  defense  by  address- 
ing his  opponent :  — 

"Mr.  Kiefe  O'Kiefe, 
I  see  by  your  brief  o'brief 
That  you  are  a  thief  o'thief,"  — 

which  so  disconcerted  Mr.  O'Kiefe  and  so  tickled  the 
jury  that  a  verdict  was  returned  for  the  defendant.  At 
least  there  was  wit  in  this  case  of  argumentum  ad  homi- 
nem,. Any  argument  in  which  there  is  appeal  to  motives 
and  facts  which  do  not  bear  upon  the  objective  truth 
of  the  position  at  issue  can  be  classed  under  this  title, 
(6)  Argumentum  ad  populum  is  an  appeal  to  the 


IM  THE  ESSENTIALS  OF  LOGIC 

feelings,  passions,  and  prejudices  of  the  group  ad- 
dressed instead  of  to  the  intellect.  Almost  all  political 
speeches  and,  I  fear,  nearly  all  writings  which  have 
become  popular  in  times  of  excitement,  have  contained 
an  ingredient  of  emotional  incitement.  The  logician 
must  follow  the  psychologist  in  the  study  of  crowd 
psychology.  He  will  then  better  know  the  power  of 
suggestion.  The  individual  thinks  most  clearly  and  in- 
dependently when  he  is  alone.  Let  him  be  on  his  guard 
against  suggestions  of  an  emotional  sort  which  do  not 
leave  a  deposit  of  definable  ideas.  The  thinker  needs  the 
will  to  analyze  and  the  power  to  put  passion  and  preju- 
dice far  away  from  him.  Let  him  remember  that  we  call 
*  enthusiasm '  in  ourselves  and  those  who  think  like  us 
what  we  call  '  fanaticism '  in  our  opponents.  The  ideal 
of  objectivity  is  not  a  bad  thing  to  set  before  one. 

The  best  instance  in  literature  of  argumentum  ad 
populum^  according  to  one  writer,^  is  Anthony's 
speech  to  the  Roman  mob  in  Shakespeare's  Julius 
Ccesar.  Let  the  student  pick  up  his  high-school  copy 
and  re-read  the  passage. 

A  species  of  argumentum  ad  populum  sometimes  re- 
ferred to  is  argumentum,  ad  misericordiam,  an  appeal 
to  pity  or  sympathy  for  a  cause  or  person  when  the 
facts  do  not  warrant  it.  We  Americans  are  soft-hearted 
and  sometimes  foolishly  sentimental. 

(c)  Argumentum  ad  ignorantiam  consists  in  the 
attempt  to  throw  the  burden  of  disproof  upon  the  other 
party  to  an  argument.  To  maintain  that  telepathy  is 
true  just  because  it  cannot  be  positively  disproved  is 
an  example  of  such  a  policy.  Mystics  are  constantly 

*  Taylor,  Elementary  Logic,  p.  180. 


FALLACIES  IN  ARGUMENTATION  155 

resorting  to  this  fallacy.  As  Creighton  points  out,  the 
reasoning  seems  to  be  as  follows :  — 

It  is  not  impossible  that  this  is  so; 
What  is  not  impossible  is  possible; 
Therefore  it  is  possible  that  this  is  so; 

Mere  abstract  possibility  is  not  enough ;  there  must  bo 
some  evidence  of  a  factual  character. 

(d)  Argumentum  ad  vericundiam  is  an  appeal  to  a 
man's  modesty  in  the  face  of  the  reverence  people  feel 
for  authority  and  tradition.  It  is  fallacious  because  it 
involves  the  refusal  to  examine  a  case  on  its  real  merits 
and  the  willingness  to  give  more  weight  to  the  ipse 
dixit  of  accepted  authorities  than  to  reason  and  fact. 
This  fallacy  is  rooted  in  the  conservative  and  conform- 
ist instincts  of  society.  Locke  felt  the  weight  of  the 
scholasticism  of  his  day  and  his  quaintly  phrased  pro- 
test is  well  worth  quoting :  "  When  men  are  established 
in  any  kind  of  dignity,  it  is  thought  a  breach  of  mod- 
esty for  others  to  derogate  any  way  from  it,  and  ques- 
tion the  authority  of  men  who  are  in  possession  of  it. 
This  is  apt  to  be  censured,  as  carrying  with  it  too  much 
pride,  when  a  man  does  not  readily  yield  to  the  deter- 
mination of  approved  authors,  which  is  wont  to  be  re- 
ceived with  respect  and  submission  by  others."  We 
must  give  weight  to  the  views  of  men  with  established 
reputations,  but  there  is  no  obligation  to  be  too  docile. 

Another  form  of  the  same  fallacy  is  the  tendency  to 
transfer  reputation  from  one  field  to  another.  To  quote 
a  famous  inventor  on  a  point  of  theology,  an  energetic 
business  man  on  problems  of  broad  statesmanship,  or 
an  explorer  on  questions  of  social  ethics  is  to  commit 
this  fallacy.  A  man  may  be  competent  in  one  field  and 


156  THE  ESSENTIALS  OF  LOGIC 

have  no  special  competence  in  another.  The  logician 
must  try  to  hold  before  the  mind  the  meaning  and  con- 
ditions of  competence.  To  tell  what  constitutes  proof 
is  also  to  tell  what  is  not  proof. 

4.  Irrelevant  Conclusion  consists  in  proving  some- 
thing different  from  the  actual  point  at  issue.  It  is  an 
evasion  or  ignoring  of  the  proposition  to  be  proved. 
"  Instead  of  proving  that  '  this  prisoner  has  committed 
an  atrocious  fraud,'  you  prove  that  the  fraud  he  ia 
accused  of  is  atrocious :  instead  of  proving  (as  in  the 
well-known  tale  of  Cyrus  and  the  two  coats)  that  the 
taller  boy  had  a  right  to  force  the  other  boy  to  exchange 
coats  with  him,  you  prove  that  the  exchange  would  have 
been  advantageous  to  both :  instead  of  proving  that  the 
poor  ought  to  be  relieved  in  this  way  rather  than  in 
that,  you  prove  that  the  poor  ought  to  be  relieved."  ^ 

This  fallacy  is  most  easily  committed  in  a  long  argu- 
ment in  which  the  original  question  passes  from  the 
mind  in  the  heat  of  the  debate.  One  point  leads  to  an- 
other, and,  if  some  one  of  the  contestants  is  not  clear- 
headed, the  concluding  thesis  is  apt  to  be  decidedly  differ- 
ent from  the  beginning  one.  "  The  person  who  commits 
the  fallacy  of  irrelevancy  is,  of  course,  quite  unaware 
of  his  error,  unless  his  purpose  be  to  mislead.  He  does 
not  see  that  the  proposition  which  he  proves  is  related 
to  the  point  at  issue  only  through  a  questionable  assump- 
tion. But  in  criticizing  an  irrelevant  argument  it  is  not 
necessary  to  point  out  the  nature  of  the  assumption 
which  underlies  the  argument.  Merely  to  show  that 
what  is  proved  is  not  what  ought  to  be  proved  or  what 
is  supposed  to  be  proved,  answers  the  purpose  of  criti- 
*  Whately,  Elements  of  Logic. 


FALLACIES  IN  ARGUMENTATION  157 

clsm.  'True,  but  irrelevant,'  is  often  the  most  concise 
and  effectual  criticism.  'Thus,  when  in  a  discussion 
one  party  vindicates,  on  the  ground  of  general  expedi- 
ency, a  particular  instance  of  resistance  to  government 
in  a  case  of  intolerable  oppression,  the  opponent  may 
gravely  maintain  that  we  ought  not  to  do  evil  that  good 
may  come  —  a  proposition  which,  of  course,  had  never 
been  denied,  the  point  in  dispute  being  whether  resist- 
ance in  this  particular  case  were  doing  evil  or  not.  Or 
again,  by  way  of  disproving  the  assertion  of  the  right 
of  private  judgment  in  religion,  one  may  hear  a  grave 
argument  to  prove  that  it  is  impossible  every  one  can 
be  right  in  his  judgment.'  The  first  of  these  arguments 
assumes,  as  a  second  premise,  that  '  this  is  a  case  of 
doing  evil  that  good  may  come ' ;  while  the  second  takes 
for  granted  that  'if  every  one  cannot  be  right  in  his 
judgment,  then  private  judgment  should  not  be  per- 
mitted.' These  assumptions,  however,  are  highly  ques- 
tionable, and  until  they  are  proved  the  arguments  are 
beside  the  point."  ^ 

All  who  have  argued  much  with  people  are  aware  of 
how  difficult  it  is  to  keep  their  attention  fixed  on  the 
point  which  first  arose  for  discussion.  This  tendency  to 
wander  off  the  track  is  the  psychological  cause  of  such 
irrelevancies  as  do  not  have  a  sophistic  origin. 

5.  Non  sequitur  is  the  name  usually  now  given  to  a 
conclusion  which  does  not  follow  from  the  premises. 
The  premises  may  be  quite  true,  but  they  do  not  lead 
to  the  proposition  which  is  attached  beneath  them.  In 
the  case  of  this  fallacy,  as  in  practically  all  of  those 
which  come  under  the  caption,  '  Unwarranted  Assump- 
*  Bode,  An  Outline  of  Logic,  pp.  103-04. 


158  THE  ESSENTIALS  OF  LOGIC 

tion,'  the  argument  in  which  it  occurs  is  nearly  always 
long-winded.  If  we  are  not  very  much  interested  in  the 
assumption,  or  if  we  are  not  inclined  to  be  analytic,  a 
boldly  advanced  conclusion  may  be  accepted  at  its  face 
value.  The  following  illustration  of  De  Morgan's  is  a 
fair  sample:  — 

Episcopacy  is  of  Scripture  origin. 

The  Church  of  England  is  the  only  Episcopal  Church  in  Eng- 
land. 

Therefore,  the  church  established  is  the  church  that  should  be 
supported. 

I  am  willing  to  hazard  the  opinion,  that  such  an  argu- 
ment, extended  over  many  pages  by  means  of  historical 
details,  would  convince  those  who  were  already  favor- 
ably inclined. 

Conclusion.  The  chief  advantage  in  a  summary  dis- 
cussion of  the  fallacies  lies  in  the  training  of  the  atten- 
tion it  involves.  It  is  a  well-known  principle  of  psy- 
chology that  we  can  see  best  what  we  are  looking  for. 
Now,  when  we  feel  that  an  argument  is  fallacious,  it  is 
of  great  assistance  to  have  in  mind  certain  general 
types  of  fallacy  which  are  possibly  relevant.  Once  the 
classification  is  made,  a  standard  interpretation  and  de- 
scription of  the  fault  is  within  our  grasp. 

REFERENCES 

Bode,  An  OtUline  of  Logic,  chap.  vni. 
Creighton,  An  Introductory  Logic,  chap.  xn. 
Sidgwick,  Fallacies. 
Whately,  Elements  of  Logic,  bk.  m. 


CHAPTER  XV 

THE  NATURE  OF  INDUCTION 

Induction  and  Deduction.  Very  often  in  the  his- 
tory of  a  science,  inappropriate  terms  fasten  themselves 
on  the  terminology  and  are  with  difficulty  removed. 
Logic  presents  us  with  such  a  case  which  is  of  the  nature 
of  a  false  contrast.  Until  very  recently,  it  has  been  cus- 
tomary to  divide  logic  into  two  distinct  parts  called,  re- 
spectively, 'deductive'  and  'inductive'  logic.  But  it  is 
being  ever  more  clearly  realized  that  this  division  is  not 
satisfactory.  What  has  been  called  '  inductive  logic '  is 
really  the  logic  of  scientific  method  or  the  logic  of  all  con- 
tinuous and  systematic  investigation  in  a  comparatively 
new  field  where  principles  are  still  to  be  discovered. 
And  the  logic  of  systematic  investigation  deals  with 
the  whole  of  concrete  reasoning  ;  it  concerns  itself  with 
the  discovery  offacts^  their  classification^  correlationy 
and  explanation. 

If  logic  is  the  science  of  correct  reasoning,  it  must 
examine  the  principles  and  methods  used  in  such  sys- 
tematic investigation.  It  must  study  the  nature  of  syste- 
matic inference  from  facts  and  the  construction  of  sys- 
tems of  knowledge  as  well  as  the  more  formal  principles 
of  classification,  definition,  and  syllogistic  argumenta- 
tion. Logicians  have  realized  this  necessity  and  have 
given  increasing  attention  to  the  larger  field  thus  opened. 
As  a  consequence,  every  recent  text  devotes  much  of  its 
space  to  scientific  method  and  to  the  dangers  which  con- 
front the  various  stages  of  concrete  inference. 


160  THE  ESSENTIALS  OF  LOGIC 

Now,  when  we  examine  concrete  reasoning  which 
does  not  take  its  facts  and  principles  for  granted,  we 
discover  that  it  includes  both  induction  and  deduction. 
These  are  really  supplementary  and  inseparable  phases 
of  any  complete  act  of  reasoning.  The  mind  passes  back 
and  forth  between  fact  and  theory,  evidence  and  infer- 
ence, and,  in  so  doing,  both  elements  are  modified.  In 
other  words,  principles  and  hypotheses  are  always  ten- 
tative and  experimental,  while  facts  need  selection  and 
interpretation. 

The  term  'induction  '  is  often  used  roughly  for  the 
passage  from  facts  and  less  general  propositions  to  laws 
and  more  general  propositions ;  while  '  deduction '  refers 
to  the  process  of  analyzing  ideas  and  using  them  in  the 
interpretation  of  facts.  As  we  proceed,  we  shall  realize 
ever  more  clearly  that  the  solution  of  any  problem  in- 
volves the  continuance  of  this  double  movement  in  the 
course  of  which  facts  are  gathered,  selected,  and  inter- 
preted, and  principles  are  suggested  and  developed.  In- 
duction is,  then,  only  a  phase  of  concrete  reasoning  or 
investigation ;  it  is  not  a  process  which  can  exist  apart. 
But  because  we  have  neglected  this  phase,  relatively,  up 
to  now  and  have  laid  stress  upon  language,  definition, 
and  the  syllogism,  we  must  emphasize  it  in  the  follow- 
ing chapters. 

A  Glance  at  the  History  of  Logic.  What  we 
have  wished  to  point  out  is  that  the  terms,  '  deductive ' 
and  '  inductive,'  were  applied  to  the  older  and  newer 
phases  of  logic  as  the  result  of  an  historical  accident 
and  that  they  are  misnomers.  The  older  logic  tended 
to  be  static  and  to  stress  consistency  and  implication, 
while  the  newer  developments  were  filled  with  the  spirit 


THE  NATURE  OF  INDUCTION  161 

of  science  and  stressed  its  methods  and  mode  of  inves- 
tigation ;  the  older  logic  was  one  of  consistency  and 
order,  the  newer  was  one  which  concerned  itself  with 
the  laws  of  systematic  and  progressive  inference.  Now, 
the  syllogism,  which  shows  how  a  conclusion  follows  in- 
evitably from  the  subsumption  of  an  instance  under  a 
rule,  was  the  dominant  element  in  the  older  logic  and 
this  was  therefore  called  '  deductive ' ;  the  movement 
from  fact  to  law  was  the  conspicuous  feature  of  the 
newer  developments  and  the  resultant  logical  doctrines 
were  classified  together  as  '  inductive.'  Thus  these  terms 
stood  for  an  historical  contrast. 

But  this  historical  contrast  has  lost  its  sharpness  with 
the  lapse  of  time.  There  is  no  longer  need  to  thunder 
against  the  scholastics  as  did  Locke  and  Francis  Bacon. 
Logic  is,  after  all,  one  science  and  not  two.  The  old 
factions  have  disappeared,  and  thinkers  on  logic  see 
clearly  that  consistency  and  growth  are  not  opposed  to 
each  other.  The  older  logic  has  consented  to  be  modi- 
fied by  the  spirit  of  the  new.  Logic  has  become  less 
formal  all  along  the  line,  and  lays  more  stress  upon  the 
material  of  thought  and  the  importance  of  purpose- 
Since  we  have  not  taken  much  space  for  the  history 
of  our  subject,  a  brief  reference  to  the  purposes  domi- 
nating logic  at  different  epochs  may  be  advisable.  "  Per- 
haps the  simplest  way  of  disentangling  the  leading 
features  of  the  departments  of  Logic  is  to  take  them  in 
relation  to  historical  circumstances.  These  features  are 
writ  large,  as  it  were,  in  history.  If  we  recognize  that 
all  bodies  of  doctrine  have  their  origin  in  practical 
needs,  we  may  conceive  different  ages  as  controlled 
each  by  a  distinctive  spirit,  which  issues  its  mandate 


162  THE  ESSENTIALS  OF  LOGIC 

to  the  men  of  the  age,  assignmg  to  them  their  distinc- 
tive work.  The  mandate  issued  to  the  age  of  Plato  and 
Aristotle  was,  Bring  your  beliefs  into  harmony  one 
with  another.  The  Aristotelian  logic  was  framed  in  re- 
sponse to  this  order :  its  main  aim  was  to  devise  instru- 
ments for  making  clear  the  coherence,  the  concatena- 
tion, the  mutual  implication  of  current  beliefs.  The 
mandate  of  the  Mediaeval  Spirit  was,  Bring  your  be- 
liefs into  harmony  with  dogma.  The  mediaeval  logic 
was  contracted  from  Aristotle's  under  this  impulse. 
Then,  as  science  developed,  a  new  spirit  was  roused  the 
mandate  of  which  was.  Bring  your  beliefs  into  har- 
mony with  facts.  It  was  under  this  impulse  that  a  body 
of  methodical  doctrine  vaguely  called  Induction  gradu- 
ally originated."  ^ 

Now,  the  first  and  last  mandates,  at  least,  are  perma- 
nent ones  which  will  always  correspond  to  a  need  of 
human  life.  Must  we  not  always  try  to  bring  our  beliefs 
into  harmony  with  one  another  and  with  fact  ?  In  exposi- 
tion there  is  a  good  pedagogical  reason  for  treating  the 
logic  of  consistency  first ;  it  is  such  a  systematic  body 
of  doctrine  pivoting  around  the  syllogism.  But  in  the 
logician's  thought  it  must  be  brought  into  touch  with 
concrete  reasoning  in  order  to  gain  in  vitality.  The 
student,  also,  must  be  prepared  to  make  this  synthesis. 

The  Function  of  the  Syllogism.  The  chief  aim  of 
logic  for  many  centuries  was,  then,  to  determine  the 
conditions  of  correct  conclusion  from  accepted  premises. 
Because  of  this  limited  aim  the  syllogism  was  the  pivot 
around  which  logical  analysis  turned.  This  simplifica- 
tion of  logic  had  its  advantages,  but  likewise  its  disad- 
^  Minto,  Logic,  Inductive  and  Deductive,  pp.  243-44. 


THE  NATURE  OF  INDUCTION  163 

vantages.  Because  the  syllogism  was  not  seen  in  its 
larger  setting  as  only  a  part  of  actual  reasoning,  it  was 
formalized  and  mechanized.  The  chief  difficulties  of 
creative  thinking  were  ignored.  While  the  keener 
minds  were  aware  that  it  gave  only  a  logic  of  consist- 
ency and  order,  the  majority  deluded  themselves  into 
assuming  that  it  was  an  instrument  of  truth  and  of 
genuine  inference.  This  misinterpretation  was,  how- 
ever, due  largely  to  the  time-spirit  of  dogmatism  which 
prevailed  for  so  long  a  period.  With  the  advent  of  sci- 
ence, logic  went  into  the  melting-pot  and  is  only  gradu- 
ally re-forming  in  the  mould  of  a  wider  outlook  and  a 
truer  perspective.  The  syllogism  still  remains  intact, 
but  a  juster  view  of  its  function  is  held.  It  is  now  seen 
that  its  function  and  even  its  character  depend  upon 
the  purpose  which  is  uppermost. 

When  the  purpose  is  the  limited  one  of  testing  the 
consistency  of  a  given  argument,  the  syllogism  is  a 
valuable  instrument.  It  offers  a  technique  by  which  the 
argument  can  be  analyzed  and  its  parts  seen  in  their 
mutual  relations.  We  can  decide  whether  all  the  ele- 
ments of  a  complete  argument  are  present,  whether  the 
terms  are  really  only  three  in  number,  whether  the  mid- 
dle terra  has  the  same  meaning  in  the  two  premises, 
whether  the  conclusion  follows,  etc.  In  short,  the  syllo- 
gism and  its  theory  presents  the  would-be  analyst  with 
satisfactory  methods  for  his  task.  He  knows  what  to 
demand  and  where  the  dangers  lie.  Relatively  to  this 
purpose,  the  syllogism  can  no  more  be  outgrown  than 
human  thought  itself. 

But  this  purpose  is,  after  all,  a  narrow  one.  We  are 
more  frequently  interested  to-day  in  the  increase  of 


164  THE  ESSENTIALS  OF  LOGIC 

knowledge  and  in  its  factual  verification.  We  want  to 
see  how  knowledge  grows  through  investigation  and  the 
formation  of  hypotheses.  We  are  more  inclined  to  go 
back  of  the  premises  of  an  argument  and  to  consider 
principles  for  which  evidence  is  not  advanced  as  dogmas. 
Moreover,  probability  plays  a  larger  part  to-day  than 
ever  before,  and  it  will  be  remembered  that  the  syllo- 
gism is  suited  only  to  certainty.  Hence  argument  is 
not  so  easy  a  matter  as  it  once  was.  Not  only  must  an 
argument  be  self-consistent ;  it  must  also  be  consistent 
with  the  facts.  But  purposes  can  coexist ;  the  narrower 
ideal  of  formal  consistency  has  its  validity  just  as  has 
the  wider  purpose.  The  wider  purpose  must  be  able  to 
include  the  narrower. 

When  the  syllogism  is  a  part  of  inductive-deductive 
reasoning,  the  premises  are  essentally  tentative :  they 
lead  to  a  certain  conclusion  ;  but  if  this  conclusion 
does  not  agree  with  the  facts,  the  premises  must  be 
modified.  The  syllogism  is  a  phase  of  a  larger  process. 
We  shall  understand  this  aspect  of  the  case  better 
when  we  come  to  consider  the  part  played  by  hypothe- 
ses in  modem  science.  It  is  important  to  us  at  present 
chiefly  as  showing  how  the  older  doctrines  are  being 
modified  by  a  larger  setting. 

Why  the  Syllogism  is  only  a  Fart  of  Reasoning. 
In  the  formal  doctrine  of  the  syllogism,  the  most  diffi- 
cult problems  of  actual  thinking  are  disregarded.  If 
your  opponent  is  kind  enough  to  grant  you  certain 
premises,  he  is  undoubtedly  obliged  to  admit  the  truth 
of  the  implied  conclusion.  But  whence  do  these  prem- 
ises come?  And  is  your  opponent  obliged  to  admit 
their  truth?    If  he  does  not,  the  argument  is  at  a 


THE  NATURE  OF  mDUCTION  165 

standstill  until  premises  are  agreed  upon.  Otherwise, 
the  syllogism  involves  a  begging  of  the  question.  It  is 
obvious  that  the  syllogism  is  a  part  of  a  larger  whole 
unless  appeal  to  intuition  is  permitted. 

Let  us  verify  this  conclusion  by  an  examination  of 
the  three  kinds  of  syllogism.  The  categorical  syllogism 
deals  with  classes,  but  it  does  not  tell  us  how  classes 
are  formed  and  tested.  Yet  such  formation  and  testing 
constitute  one  of  the  most  difficult  tasks  of  science.  If 
we  bear  in  mind  the  fact  that  real  argument  arises 
only  as  the  result  of  doubt  and  perplexity,  we  can  ap- 
preciate the  importance  of  the  processes  largely  pre- 
liminary to  the  syllogism.  All  syllogisms  require  at 
least  one  universal  proposition,  but  universal  proposi- 
tions do  not  grow  on  every  bush. 

The  hypothetical  syllogism  is  in  essentially  the  same 
situation.  The  major  premise  states  a  universal  or  nec- 
essary connection  between  an  antecedent  and  a  conse- 
quent. But  such  principles  must  first  be  achieved,  and 
they  represent  the  maturity  of  a  science  rather  than 
its  beginning.  Otherwise,  they  are  essentially  experi- 
mental. So  long  as  the  major  is  tentative,  the  conclu- 
sion is  a  challenge  to  fact ;  but  then  the  syllogism  be- 
comes a  part  of  a  progressive  movement  of  knowledge. 

The  disjunctive  syllogism  is  obviously  in  the  same 
situation.  The  alternatives  must  be  complete  and  mutu- 
ally exclusive.  But  the  attainment  of  such  alternatives 
in  any  new  field  is  not  an  easy  matter.  Of  course,  it 
is  an  easy  matter  to  work  up  such  alternatives  as 
honest  and  dishonest,  truthful  and  untruthful.  These 
are  simple  contradictories  and  are  not  apt  to  lead  to 
confusion.    But  to  prove  that  certain  theories  alone 


166  THE  ESSENTIALS  OF  LOGIC 

hold  the  field  is  an  achievement  lying  back  of  the 
disjunctive  syllogism. 

Steps  in  Systematic  Investigation.  There  are 
at  least  four  stages  in  any  systematic  investigation. 
These  have  been  stated  variously,  and  certain  writers 
have  felt  themselves  compelled  to  break  up  one  or 
more  of  the  stages  into  parts.  I  must  warn  the  student 
against  supposing  that  these  stages  are  temporally  dis- 
tinct so  that  one  stage  can  be  completed  before  the 
next  begins.  The  mind  of  the  true  investigator  keeps 
them  as  contemporaneous  as  possible,  and  passes  up 
and  down  his  chain  of  reasoning  from  fact  to  theory 
and  from  theory  to  fact.  In  a  sense,  the  active  thinker 
observes  while  he  theorizes  and  theorizes  while  he 
observes. 

The  first  stage  in  systematic  investigation  is  obser- 
vation ;  the  second  is  the  formation  of  hypotheses  ;  the 
third  is  the  development  of  these  hypotheses  ;  and  the 
fourth  is  their  progressive  testing  and  verification  by 
renewed  observation.  These  steps  are  fairly  separable 
for  logical  analysis  though  they  do  not  exist  in  such 
isolation  in  actual  investigation.  Each  stage  is  con- 
fronted by  characteristic  dangers  and  involves  logical 
and  psychological  principles  of  importance.  Only  by 
means  of  this  massive  and  systematic  advance  with  its 
constant  hazards  is  new  knowledge  obtained. 

Three  Elements  in  Investigation.  There  are 
three  elements  or  distinguishable  mental  processes  in  all 
investigation.  We  may  call  the  first  the  inductive  ele- 
ment par  excellence.  In  both  observation,  the  begin- 
ning of  investigation,  and  verification,  its  end,  the 
stress  is  laid  upon  facts.    The  essential  principle  of 


THE  NATURE  OF  INDUCTION  167 

this  element  in  the  attainment  of  knowledgt  is  fidelity 
to  relevant  fact.  Science  has  always  stressed  fact  as 
the  beginning  and  only  firm  foundation  of  knowledge. 

The  second  element  is  the  formation  of  hypotheses. 
The  creative  investigator  must  be  capable  of  making 
fruitful  conjectures  as  to  the  relations  which  hold  be- 
tween facts  or  lie  back  of  them.  He  must  have  what 
one  psychologist  speaks  of  as  a  creative  imagination. 
Francis  Darwin  in  his  biography  of  his  father  remarks 
as  follows :  "  He  often  said  that  no  one  could  be  a 
good  observer  unless  he  was  an  active  theorizer.  This 
brings  me  back  to  what  I  said  about  his  instinct  for 
arresting  exceptions  ;  it  was  as  though  he  were  charged 
with  theorizing  power  ready  to  flow  into  any  channel 
on  the  slightest  disturbance,  so  that  no  fact,  however 
small,  could  avoid  releasing  a  stream  of  theory,  and 
thus  the  fact  became  magnified  into  importance."  We 
shall  have  much  to  say  of  this  constructive,  conjectural 
element  as  we  proceed. 

The  third  element  is  the  deductive  reasoning  out  of 
the  implications  of  hypotheses  and  theories  to  see  what 
they  imply  in  the  light  of  knowledge  already  possessed. 
Some  writers  in  logic  speak  of  this  element  as  '  de- 
ductive inference ' ;  others  speak  of  it  as  '  reasoning.' 
In  any  case,  the  significance  of  the  hypothesis  is  devel- 
oped as  completely  as  possible  and  its  implications 
noted.  These  implications  lead  back  to  the  sphere  of 
fact  again  and  so  we  return  to  the  inductive  element. 

The  Problem  of  Generalization.  As  has  been  well 
said,  syllogism  never  generalizes.  How,  then,  do  we 
secure  universal  or  semi-universal  propositions  to  serve 
as  premises  ?  The  difficulty  arises  from  the  fact  that 


168  THE  ESSENTIALS  OF  LOGIC 

experience  gives  us  only  particular  events  and  things. 
We  note  that  this  medicine  seems  to  have  a  beneficial 
effect,  and  that  this  piece  of  metal  has  certain  proper- 
ties ;  but  how  do  we  go  beyond  the  instance  to  a  rule  ? 
We  must,  first  of  all,  be  careful  to  set  the  problem 
correctly.  Modern  psychology  informs  us  that  every 
instance  is  interpreted  in  the  light  of  past  experience 
at  the  time  it  enters  consciousness.  Things  and  events 
are  noted  as  members  of  a  familiar  class  or  as  members 
of  a  potential  class.  Observation  and  generalization, 
perce|)tion  and  interpretation,  sensation  and  association 
go  hand  in  hand.  We  interpret  as  we  perceive  and  gen- 
eralize as  we  observe.  The  mind  is,  moreover,  selective 
and  stresses  what  is  regarded  as  important  or  even  essen- 
tial. If  this  medicine  cures  an  ill,  then  curing  this  kind 
of  ill  is  an  essential  property  of  this  kind  of  medicine. 
We  expect  classes  and  other  instances.  Why?  Because 
it  is  the  very  nature  of  the  mind  to  note  similarities 
and  differences  and  so  to  classify.  "  It  is  for  the  sake 
of  generalization  that  we  observe  at  all,  and  the  very 
act  of  observing  intelligently  is  nothing  else  than  the 
act  of  generalizing  from  what  we  observe."  We  do  not 
so  much  pass  from  particular  instance  to  particular  in- 
stance as  from  a  beginning  class  to  a  growing  class. 

A  little  reflection  must  convince  us  that  the  mental 
process  leading  to  generalization  does  not  depend  upon 
the  application  of  any  consciously  held  principle —  even 
though  its  logical  validity  may  imply  some  such  princi- 
ple. As  writers  since  the  days  of  David  Hume  have 
pointed  out,  the  child  unconsciously  generalizes  things 
and  events  and  builds  up  practical  rules  to  act  upon. 
Wild  plums  are  very  sweet  when  they  are  ripe ;  fish 


THE  NATURE  OF  INDUCTION  169 

bite  best  on  cloudy  days ;  the  river  will  be  swollen  after 
a  rain ;  a  circus  always  has  a  band,  etc.  Such  classifica- 
tions are  gradually  built  up  because  the  process  of  gen- 
eralization continually  repeats  itself  in  our  minds  ;  and 
our  lives  are  guided  at  every  moment  by  the  maxims 
and  rules  thus  obtained.  What  science  does  is  to  ex- 
tend experience  and  to  control  it  by  completer  analysis 
and  experiment.  It  does  reflectively  and  methodically 
what  common  sense  has  been  doing  aU  along. 

This  tendency  to  put  two  and  two  together,  to  regard 
one  thing  as  an  indication  of  another,  is  evidently  a  part 
of  our  mental  constitution.  This  linkage  of  terms  com- 
bined with  the  recognition  of  likenesses  and  differences 
accounts  for  a  large  share  of  what  we  call  reasoning. 
Professor  Dewey  goes  so  far  as  to  assert  that  the  estab- 
lishment of  one  thing  as  a  sign  of  another  is  the  cen- 
tral factor  of  thinking.  "Reflection  thus  implies  that 
something  is  believed  in  (or  disbelieved  in),  not  on  its 
own  direct  account,  but  through  something  else  which 
stands  as  witness,  evidence,  proof,  voucher,  warrant ; 
that  is,  as  ground  of  belief.  At  one  time,  rain  is  actu- 
ally felt  or  directly  experienced ;  at  another  time,  we 
infer  that  it  has  rained  from  the  looks  of  the  grass  and 
trees,  or  that  it  is  going  to  rain  because  of  the  condi- 
tion of  the  air  or  the  state  of  the  barometer.  At  one 
time,  we  see  a  man  (or  suppose  we  do)  without  any 
intermediary  fact ;  at  another  time,  we  are  not  quite  sure 
what  we  see,  and  hunt  for  accompanying  facts  that  will 
serve  as  signs,  indications,  tokens  of  what  is  to  be  be- 
lieved." 1 

The  Implication  of  Q-eneralization.    Logic  does 

1  Dewey,  How  We  Think,  p.  8. 


170  THE  ESSENTIALS  OF  LOGIC 

not  impugn  the  act  of  generalization,  but  tries  to  under- 
stand what  takes  place  and  what  principle  is  implied. 
It  is  evident  that  an  event  acquires  meaning  as  a  sign 
of  another  event  so  that  an  internal  relation  between 
them  is  developed  in  the  mind.  It  is  also  apparent  that 
any  one  event  is  regarded  as  typical  of  a  class.  We 
pass  quickly  from  this  event  to  an  event  of  this  class 
as  soon  as  our  minds  are  preparing  to  generalize.  Sup- 
pose a  savage  goes  out  on  a  hunt  for  game,  and,  as  he 
steps  into  the  forest,  a  rabbit  crosses  his  path.  It  hap- 
pens that  he  has  no  luck  that  day.  If  he  is  supersti- 
tious, he  is  liable  to  connect  this  lack  of  success  with  the 
appearance  of  the  rabbit.  But  he  has  no  reason  to  sup- 
pose that  there  is  anything  peculiar  about  tliis  particular 
rabbit ;  hence  it  sinks  back  into  the  class.  It  is  the  rab- 
bit as  a  recognizable  class  of  animals  that  presages  bad 
luck.  Unless  there  is  strong  reason  to  the  contrary,  the 
individual  instance  tends  to  be  merged  in  the  idea  of 
the  class.  Psychologically,  the  class  is  as  primitive  as 
the  individual. 

But  if  the  logician  does  not  impugn  the  tendency  to 
generalize,  he  is  aware,  nevertheless,  that  a  principle  is 
involved  which  must  be  valid  if  the  generalization  is 
valid.  This  principle  or  postulate  is  usually  called  the 
*  Principle  of  the  Uniformity  of  Nature.'  We  assume^ 
consciously  or  unconsciously,  that  there  are  universal 
connections  or  relations  in  nature.  This  assumption, 
when  formulated  explicitly,  is  suggested  by  the  way  the 
mind  works  and  the  degree  to  which  nature  seems  to 
recognize  the  tendency  to  relate  terras  as  invariable 
signs  of  one  another.  But  logicians  have  come  to  the 
conclusion  that  the  principle  cannot  be  proved  by  expe- 


THE  NATURE  OF  INDUCTION  171 

rience,  but  can  only  be  relatively  confirmed  by  it.  For 
this  reason,  it  is  frequently  called  a  '  postulate.' 

How  Generalization  differs  from  Expectation. 
Animals  develop  expectations  in  much  the  same  way 
that  human  beings  do.  A  doctor's  horse  expects  to  turn 
in  at  a  certain  farmhouse  because  it  has  done  so  on 
previous  trips.  A  dog  anticipates  a  walk  when  his  mas- 
ter takes  down  his  hat  from  the  wall.  The  formation 
of  associations  of  this  character  is  natural  to  the  mind 
at  fairly  low  levels  as  well  as  at  the  human  level.  Is 
generalization  more  than  this  ?  Though  based  on  it  in 
part,  it  certainly  goes  beyond  mere  expectation.  Other 
mental  processes  than  those  of  association  enter  in.  The 
aiiimal  glides  from  the  one  event  to  the  other  without 
holding  them  both  before  the  mind  as  distinct  objects  of 
attention.  But  man  does  hold  both  terms  of  the  rela- 
tion before  his  mind  at  one  and  the  same  time,  and 
makes  them  and  their  internal  connection  a  single  com- 
plex object  of  thought.  This  the  animal  cannot  do.  We 
may  say,  then,  that  generalization  is  a  higher  develop- 
ment than  expectation  and  depends  upon  the  capacity 
to  conceive  two  events  as  classes  and  to  relate  them  in- 
ternally as  somehow  bound  together.  A  generalization 
is  a  more  or  less  explicit  assertion  that  two  terms  are 
related. 

The  Importance  of  Generalization.  It  may  not 
be  amiss  to  call  attention  once  more  to  the  importance 
of  generalization.  Were  we  literally  confined  to  par- 
ticulars, we  should  be  unable  to  reason.  The  very  na- 
ture of  reasoning  is  the  passage  from  what  is  given  to 
what  is  not  directly  given.  As  we  say,  we  infer  that 
so-and-so  will  happen  because  something  else  has  oc- 


172  THE  ESSENTIALS  OF  LOGIC 

curred.  This  something  else  is  taken  as  a  sign  of  the 
event  inferred.  Thus  we  apply  rules  to  our  present  ex- 
perience in  order  to  interpret  it  and  to  pass  in  concep- 
tion beyond  it.  But  such  rules  can  come  only  from 
generalization. 

Testing  Generalizations.  While  we  cannot  prove 
the  Principle  of  the  Uniformity  of  Nature,  we  can  test 
specific  inductive  inferences  to  see  whether  they  really 
come  under  the  principle.  If  they  stand  aU  the  empiri- 
cal tests  we  can  apply,  we  call  them  laws  of  nature. 
Science  has  for  centuries  been  engaged  in  the  discovery 
of  laws  of  this  character,  laws  which  the  hasty  observa- 
tions and  inadequate  methods  of  common  sense  cannot 
discover.  The  generalizations  of  common  sense  are  rules 
and  maxims  which  hold  in  the  main  rather  than  laws 
which  are  universal  or  do  not  admit  of  exceptions.  Why 
common  sense  is  not  able  to  formulate  many  universal 
propositions  will  become  clearer  to  us  as  we  proceed. 
Its  maxims  are  not  founded  on  analytic  methods  which 
exclude  the  irrelevant.  The  strength  of  science  rests 
on  the  development  of  such  methods  and  the  technique 
which  accompanies  them.  It  is  to  the  consideration  of 
this  technique  and  these  methods  in  their  general  as- 
pects that  we  now  turn  our  attention. 

REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  ix. 

Creighton,  An  Introductory  Logic,  chap.  xni. 

Dewey,  How  We  Think,  chaps,  i  and  vn. 

Minto,  Logic,  Inductive  and  Deductive,hk.  U,  Introduction. 

Sidgwick,  The  Process  of  Argument,  chaps,  rv  and  viii. 


CHAPTER  XVI 

THE  GENERAL  METHODS  OF  SCIENCE 

Ho'w^  Science  developed.  Science  grew  to  its  pres- 
ent stature  by  the  efforts  of  men  who  attempted  to 
solve  problems  which  attracted  their  attention.  There 
was  much  groping  before  suitable  methods  and  a  fairly 
satisfactory  technique  were  worked  out.  The  simplest 
aspects  of  nature  were  attacked  before  it  was  even  pos- 
sible to  approach  the  more  complex  fields.  The  growth 
of  science  was  the  result  of  the  painstaking  care  and 
genius  of  such  men  as  Galileo,  Kepler,  Newton,  Lavoi- 
sier, Liebig,  and  others  too  numerous  to  mention. 
Their  sagacity,  fertility  of  suggestion,  experimental  in- 
genuity, and  thoroughness  led  to  the  gradual  accumu- 
lation of  facts  and  the  appearance  of  just  notions  about 
the  constitution  and  mode  of  working  of  the  inorganic 
realm.  Bit  by  bit,  problems  were  properly  defined,  in- 
vestigated, theorized  over,  experimented  upon  and  ex- 
plained. The  technique  of  measurement  was  evolved, 
mathematics  applied,  and  instruments  invented.  Thus, 
step  by  step,  facts  were  discovered  and  fundamental 
principles  like  the  *  laws  of  Kepler '  and  the  theory  of 
gravitation  of  Newton  were  enunciated.  All  this  was 
a  growth  of  the  most  subtle  kind  which  substituted  a 
world  of  laws  and  conceptual  elements  for  the  familiar 
mass  of  changing  things.  The  early  scientists  were 
confronted  by  a  world  of  happenings  and  of  unana- 
lyzed  things,  and  it  was  with  the  greatest  difficulty 


174  THE  ESSENTIALS  OF  LOGIC 

that  they  learned  how  to  handle  it  and  make  it  tell  its 
secrets.  Let  the  student  try  to  remove  from  his  thought 
of  the  world  such  ideas  as  mass,  inertia,  gravitation,  the 
laws  of  motion,  the  chemical  elements,  energy,  etc.,  and 
he  will  better  understand  how  much  he  owes  to  the 
constructive  genius  of  these  men. 

Since  our  purpose  is  to  understand,  and  do  justice 
to,  all  the  factors  in  systematic  inference,  we  must  not 
neglect  the  ways  in  which  these  typical  fathers  of  sci- 
ence made  their  contributions.  Probably  there  is  no 
better  example  for  study  than  Galileo.  "In  1581, 
while  watching  a  lamp  set  swinging  in  the  cathedral  of 
Pisa,  he  observed  that,  whatever  the  range  of  its  oscil- 
lations, they  were  invariably  executed  in  equal  times. 
The  experimental  verification  of  this  fact  led  him  to 
the  important  discovery  of  the  isochronism  of  the  pen- 
dulum." Here  we  note  the  alert  attention  ready  to 
notice  and  meditate  upon  features  of  the  surrounding 
world  which  would  escape  the  vast  majority,  and  the 
experimental  facility  which  enables  the  analyst  to  sep- 
arate out  special  factors  and  control  their  occurrence. 
During  two  years  which  he  spent  as  a  lecturer  on  math- 
ematics at  the  University  of  Pisa,  "  he  carried  on  that 
remarkable  series  of  experiments  by  which  he  estab- 
lished the  first  principles  of  dynamics  and  earned  the 
undying  hostility  of  bigoted  Aristotelians.  From  the 
leaning  tower  of  Pisa  he  afforded  to  all  the  professors 
and  students  ocular  demonstration  of  the  falsehood  of 
the  Peripatetic  doctrine  that  heavy  bodies  fall  with 
velocities  proportional  to  their  weights."  ^  Galileo  was 
a  keen  observer,  a  suggestive  interpreter,  and  a  clever 
^  JSncyclopcedia  Britannica,  art.  "  Galileo." 


THE  GENERAL  METHODS  OF  SCIENCE     175 

inventor.  He  saw  problems  and  had  the  ingenuity  to 
meet  them. 

The  Need  of  Analysis.  The  progress  of  science  evi- 
dently depends  upon  all  the  processes  by  means  of 
which  facts  are  gathered,  analyzed,  and  interpreted. 
Such  collection  of  data  involves  selection,  and  this  se- 
lection is  facilitated  by  processes  of  comparison  and 
analysis.  The  purpose  is  to  eliminate  the  irrelevant  and] 
accidental  and  to  center  attention  on  the  important^ 
and  essential.  Whatever  aids  in  this  task  is  of  primary 
importance  for  systematic  inference.  Only  after  surface 
appearances  are  passed  and  irrelevant  but  confusing 
circumstances  eliminated  can  the  problem  be  defined 
and  its  probable  answer  suggested.  Analysis  by  com- 
parison and  experimentation  is  the  pre-condition  of 
explanatory  conceptions. 

But  we  must  never  forget  that  the  determination  of 
what  is  important  and  relevant  is  no  easy  matter  and 
is,  indeed,  the  outgrowth  of  that  prior  knowledge  for 
which  the  scientist  has  served  an  apprenticeship.  Every 
problem  requires  a  more  or  less  special  method  and 
technique,  and  these  reflect  the  ideas  which  are  in  the 
mind  of  the  investigator.  If  he  have  the  wrong  notion, 
he  may  lose  much  time  and  labor  to  no  account  until 
some  fact,  or  facts,  makes  him  realize  that  he  has  been 
guided  by  a  false  conception.  Logic  can  give  no  royal 
road  to  discovery.  It  can  only  abet  the  teacher  of  sci- 
ence in  making  the  student  conscious  of  the  best  meth- 
ods, mental  habits  and  ideals  and  warning  him  against 
the  dangers  of  haste  and  dogmatism. 

The  Value  of  Technique  and  Instruments.  The 
scientific  man  is  on  his  guard  against  hasty  conclusions. 


176  THE  ESSENTIALS  OF  LOGIC 

He  knows  how  easy  it  is  to  be  led  into  errors  of  fact 
or  theory  by  his  interests  and  prejudices.  It  is  this 
awareness  of  the  difficulties  confronting  valid  induction 
that  leads  him  to  collect  so  many  facts  and  to  use  in- 
struments wherever  possible.  "  The  technique  of  scien- 
tific inquiry  thus  consists  in  the  various  processes  that 
tend  to  exclude  over-hasty  '  reading  in  '  of  meanings  ; 
devices  that  aim  to  give  a  purely  '  objective '  unbiased 
rendering  of  the  data  to  be  interpreted.  Flushed  cheeks 
usually  mean  heightened  temperature ;  paleness  means 
lowered  temperature.  The  clinical  thermometer  records 
automatically  the  actual  temperature  and  hence  checks 
up  the  habitual  associations  that  might  lead  to  error  in 
a  given  case.  All  the  instrumentalities  of  observation 
—  the  various  meters  and  -graphs  and  -scopes — fill  a 
part  of  their  scientific  role  in  helping  to  eliminate 
meanings  supplied  because  of  habit,  prejudice,  the 
strong  momentary  preoccupation  of  excitement  and  an- 
ticipation, and  by  the  vogue  of  existing  theories.  Pho- 
tographs, phonographs,  kymographs,  actinographs,  seis- 
mographs, phethysmographs,  and  the  like,  moreover, 
give  records  that  are  permanent,  so  that  they  can  be 
employed  by  different  persons  and  by  the  same  person 
in  different  states  of  mind,  i.e.,  under  the  influence  of 
varying  expectations  and  dominant  beliefs."  ^ 

The  attention  of  the  scientist  is  more  sustained  and 
his  observations  are  more  systematic  and  unprejudiced 
than  those  of  the  untrained  man.  He  possesses  a  men- 
tal technique  of  habits  as  well  as  the  technique  of  instru- 
ments. But  with  modern  methods  of  education,  no  one 
should  be  without  some  tincture  of  these  methods  and 
»  Dewey,  How  We  Think,  pp.  87-88. 


THE  GENERAL  METHODS  OF  SCIENCE    177 

attitudes.  Logic  seeks  to  inculcate  those  mental  quali- 
ties which  make  for  good  thinking,  such  as  caution,  care- 
fulness, thoroughness,  orderliness,  exactness,  critical- 
ness.  In  this  sense,  education  is  primarily  the  formation 
of  logical  dispositions,  of  "  careful,  alert,  and  thorough 
habits  of  thinking." 

The  Importance  of  Measurement  Definite  knowl- 
edge has  developed  step  by  step  with  the  power  to  meas- 
ure phenomena.  In  the  physical  sciences  at  least,  laws 
are  equations  between  the  measurable  elements  of  phe- 
nomena. Hence  the  invention  of  new  and  more  exact  in- 
struments of  measurement  has  usually  led  to  marked 
advances  in  the  analysis  of  nature.  "  It  would  be  a  mat- 
ter of  great  interest  to  trace  out  the  dependence  of  this 
vast  progress  upon  the  introduction  of  new  instruments. 
The  astrolabe  of  Ptolemy,  the  telescope  of  Galileo,  the 
pendulum  of  Galileo  and  Huygens,  the  micrometer  of 
Horrocks,  and  the  telescopic  sights  and  micrometer  of 
Gascoyne  and  Picard,  Roemer's  transit  instrument, 
Newton's  and  Hadley's  quadrant,  DoUond's  achromatic 
lenses,  Harrison's  chronometer  and  Ramsden's  dividing 
engine — such  were  some  of  the  principal  additions  to 
astronomical  apparatus.  The  result  is,  that  we  now  take 
note  of  quantities,  300,000  or  400,000  times  as  small  as 
in  the  time  of  the  Chaldeans."  ^ 

Experimentation.  The  devising  of  experiments  is 
one  of  the  important  elements  in  a  scientific  investiga- 
tion. An  experiment  works  towards  an  analysis  of  nature 
and  a  control  of  the  field  under  study  which  will  make 
the  important  facts  stand  out  clearly.  The  modern  stu- 
dent desires  to  control  the  order  of  occurrence  of  his 
1  Jevons,  The  Principles  of  Science,  vol.  i,  p.  315. 


178  THE  ESSENTIALS  OF  LOGIC 

phenomena  and  to  vary  the  factors  which  are  present. 
Under  such  conditions,  he  is  able  to  eliminate  features 
and  notice  the  effect,  and  to  introduce  new  features  and 
see  what  happens.  Within  certain  limits,  he  can  do 
with  nature  as  he  wishes  and  make  it  answer  his  ques- 
tions. Thus  experimentation  is  a  method  of  controlled 
analysis,  synthesis,  and  variation  which  enables  man  to 
make  combinations  that  coidd  never  be  observed  free  in 
nature. 

There  are  essentially  three  advantages  in  experiment. 
We  can  vary  the  combinations  and  circumstances  of 
things  at  will;  we  can  produce  factors  at  will  which  we 
:  might  have  to  wait  years  for  otlierwise  or  even  never 
obtain ;  lastly  we  can  overcome  the  rigidity  of  things  as 
Ithey  ordinarily  present  themselves.  The  following  ac- 
count of  experimentation  brings  out  very  well  its  place 
in  investigation :  "  All  inductive  methods  rest  upon  the 
regulation  of  the  conditions  of  observation  and  memory ; 
experiment  is  simply  the  most  adequate  regulation  pos- 
sible of  these  conditions.  We  try  to  make  the  observa- 
tion such  that  every  factor  entering  into  it,  together, 
with  the  mode  and  the  amount  of  its  operation,  may  be 
open  to  recognition.  Such  making  of  observations  con- 
stitutes experiment."  ^  Ingenuity  in  experimentation  is 
certainly  one  of  the  prime  qualifications  of  an  investi- 
gator in  the  physical  sciences.  Such  men  as  Faraday, 
Liebig,  Pasteur,  Darwin,  and  Davy  were  noted  for 
their  fertility  in  ideas  and  methods. 

The  first  stage  of  a  science  is  dominantly  observational 
in  its  mode  of  gathering  and  testing  facts.  Many  sciences, 
like  geology,  find  it  difficult  to  pass  beyond  this  stage 
^  Dewey,  How  We  Think,  p.  91. 


THE  GENERAL  METHODS  OF  SCIENCE     179 

because  of  the  nature  of  the  material  with  which  they 
have  to  deal.  But  the  ideal,  at  least,  in  all  the  sciences 
is  the  testing  of  hypotheses  by  carefully  planned  ob- 
servations. We  are  all  so  familiar  with  the  use  of  ex- 
periment in  physics  and  chemistry  that  we  scarcely  give 
it  enough  thought,  but  the  application  of  experimental 
methods  to  biology  and  psychology  is  newer  and  not  so 
familiar.  Yet,  in  these  fields,  also,  nature  is  being  com- 
pelled to  react  to  conditions  which  would  be  unlikely  to 
occur  apart  from  human  purpose.  It  is  evident,  then, 
that  experimentation  is  a  method  of  investigation  and 
that  it  is  the  servant  of  ideas  which  are  seeking  to  find 
themselves  verified. 

The  Use  of  Experiment  in  Biology.  Experimental 
biology  dates  back  only  a  few  decades  and  is  only  now 
being  developed  to  the  extent  it  deserves.  It  has  been 
found  that  gi'owing  organisms  can  be  interfered  with  at 
various  stages  in  a  grossly  mechanical  way  without  pre- 
venting the  production  of  normal  forms.  "  A  particu- 
larly striking  case  is  that  of  Clavellina,  an  ascidian, 
that  is  to  say,  an  animal  organism  of  considerable  com- 
plexity. *  You  first  isolate  the  branchial  apparatus  from 
the  other  part  of  the  body  (which  other  part  contains 
heart,  stomach,  and  most  of  the  intestine),  and  then 
you  cut  in  two  in  whatever  direction  you  please.  Pro- 
vided they  survive  and  do  not  die,  as  indeed  many  of 
them  do,  the  pieces  obtained  by  this  operation  will  each 
lose  its  organization  (becoming  a  mere  sphere  of  cells 
devoid  of  specialized  structure)  .  .  .  and  then  will  each 
acquire  another  one,  and  this  new  organization  is  also 
that  of  a  complete  little  Clavellina.'  "  ^ 

*  McDougall,  Body  and  Mind,  p.  240. 


180  THE  ESSENTIALS  OF  LOGIC 

Experimentation  in  Psychology.  James's  pic- 
turesque description  of  the  rise  of  experiment  in  psy- 
chology is  well  worth  quoting  in  this  connection : 
"  Within  a  few  years  what  one  may  call  a  microscopic 
psychology  has  arisen  in  Germany,  carried  on  by  exper- 
imental methods,  asking  of  course  every  moment  for 
introspective  data,  but  eliminating  their  uncertainty  by 
operating  on  a  large  scale  and  taking  statistical  means. 
This  method  taxes  patience  to  the  utmost,  and  could 
hardly  have  arisen  in  a  country  whose  natives  could  be 
bored.  Such  Germans  as  Weber,  Fechner,  Vierordt, 
and  Wundt  obviously  cannot ;  and  their  success  has 
brought  into  the  field  an  array  of  younger  experimental 
psychologists,  bent  on  studying  the  elements  of  the 
mental  life,  dissecting  them  out  from  the  gross  results 
in  which  they  are  embedded,  and  as  far  as  possible  re- 
ducing them  to  quantitative  scales.  The  simple  and 
open  method  of  attack  having  done  what  it  can,  the 
method  of  patience,  starving  out,  and  harassing  to  death 
is  tried.  .  .  .  There  is  little  of  the  grand  style  about 
these  new  prism,  pendulum,  and  chronograph-philoso- 
phers. They  mean  business,  not  chivalry."  i  The  an- 
alytic character  of  experimentation  comes  out  clearly  in 
this  quotation.  The  experimenter  tries  to  dissect  and 
abstract,  and  he  is  helped  in  his  effort  by  instruments 
and  methods  of  control. 

i  The  Statistical  Method.  In  complex  fields  science 
has  gradually  been  forced  to  methods  of  tabulation  in 
which  results  are  set  down  in  their  appropriate  places 
and  averaged.  The  observation  of  specific  things  has 
given  way  to  the  gathering  and  arrangement  of  data. 
*  Principles  of  Psychology,  vol.  i,  p.  192. 


THE  GENERAL  METHODS  OF  SCIENCE    181 

Only  after  these  data  are  collected  and  tabulated  is 
there  any  attempt  made  to  interpret  them  and  to  draw 
the  proper  inferences.  Combined  with  statistical  meth- 
ods is  the  use  of  averages  of  various  sorts,  such  as  the 
arithmetical,  the  '  weighted,'  the  geometrical,  the  mode, 
and  the  median. 

Statistical  methods  are  particularly  employed  in 
fields  where  experimental  analysis  cannot  be  obtained. 
Thus  there  is  much  use  of  statistics  in  the  social  sci- 
ences and  in  such  a  field  as  meteorology.  After  the 
'  primary  statistical  quantities  '  are  gathered,  they  must 
be  arranged  in  tables  in  such  a  manner  as  to  bring  out 
important  correlations.  As  we  shall  see  when  we  take 
up  the  method  in  more  detail,  there  are  many  possibili- 
ties of  fallacy  in  both  the  gathering  and  the  manipula- 
tion of  statistics. 

[  The  Method  of  Graphs.  When  relations  between 
variables  are  complex  and  cannot  be  easily  intuited, 
resort  is  increasingly  had  to  the  use  of  graphs.  In  a 
graph,  a  curve  is  plotted  to  bring  out  in  a  spatial  way 
the  relation  involved.  In  this  way,  the  correlation  be- 
comes visible  to  the  eye  and  is  grasped  without  dif- 
ficulty. The  interesting  thing  is,  that  such  projection 
of  variable  quantities  often  leads  to  the  discovery  of  re- 
lations which  the  investigator  would  not  otherwise  have 
noticed. 

Graphs  are  used  in  statistical  investigation  as  a  means 
of  bringing  out  the  import  of  the  data  in  a  vivid  way. 
We  are  all  familiar  with  this  use  of  diagrams  to  illus- 
trate the  comparative  populations  of  the  various  coun- 
tries, or  the  relative  sizes  of  their  armies  and  navies,  or 
the  wheat  production  in  different  years.  Investigations 


182  THE  ESSENTIALS  OF  LOGIC 

in  criminology  are  usually  condensed  by  the  aid  of 
graphs.  In  brief,  the  graphical  method  is  one  both  of 
investigation  and  of  exposition. 

The  Function  of  Hypotheses.  In  our  treatment 
of  scientific  method,  we  have  thus  far  called  attention 
to  the  more  external  processes  and  technique  which  sci- 
ence has  developed.  But  we  must  never  forget  that  these 
processes  require  an  informing  spirit  to  guide  them. 
There  must  always  be  a  purpose  at  work  and  some 
fairly  specific  problem  in  sight  before  this  machinery 
begins  to  move.  To  become  familiar  with  the  technique 
and  instrumentation  of  science  does  not  make  a  creative 
scientist ;  nor  is  it  enough  to  stare  passively  at  test- 
tubes  and  microscopes.  Facts  are  not  objects  to  be  col- 
lected like  pebbles.  They  are  not  things  which  stand 
out  in  the  environment  with  an  external  unity  and 
identity  of  their  own,  but  are  dependent  for  their  exist- 
ence, in  one  sense,  and  certainly  for  their  perception, 
upon  the  mind  of  the  investigator.  Facts  do  not  pass 
into  the  mind  ready-made,  nor  do  they  offer  themselves. 
The  scientist  must  be  on  the  watch  for  them  and  must 
aid  them  to  express  themselves.  His  mind  must  be 
sensitive  to  them.  Without  mental  activity,  it  would  be 
impossible  to  gather  facts.  Why  is  this  ?  It  is  founded 
on  the  very  nature  of  voluntai'y  attention.  We  attend 
to  what  we  are  interested  in;  other  things  pass  un- 
noticed. 

The  facts  connected  with  any  investigation  must  be 
relevant  facts.  And  this  word  gives  us  our  clue.  To  be 
relevant  is  to  be  related  to  a  purpose  and  a  set  of  ideas. 
We  must  have  some  standard  of  selection,  some  way  of 
telling  what  is  important  and  what  is  unimportant. 


THE  GENERAL  METHODS  OF  SCIENCE     183 

There  is  a  hazard  in  this,  but  the  investigator  must 
always  take  his  chance.  The  warning  that  science  gives 
by  its  history  is  general,  and  the  individual  scientist 
must  make  his  own  judgments  and  collect  his  own  in- 
stances. 

While  the  mind  must  be  active  in  observation,  it 
must  be  still  more  active,  and  certainly  more  creative, 
in  experimentation.  Some  theory  or  hypothesis  is  always 
at  the  basis  of  an  experiment.  The  experimenter  has 
some  idea  of  what  he  expects  to  find.  The  experiment 
is,  in  fact,  usually  devised  consciously  to  test  a  concep- 
tion which  has  gained  favor.  If  oxygen  is  the  essential 
factor  in  combustion,  then  its  removal  should  prevent  it. 
The  resultant  experiment  is  the  crucial  instance  for  the 
theory.  If  we  are  forced  to  deny  a  consequent,  we  are 
forced  to  deny  the  antecedent  likewise,  and  to  reject 
the  idea  which  was  gaining  ground.  It  was  in  such  a 
way  as  this  that  the  phlogiston  theory,  which  held  sway 
before  oxygen  was  discovered,  was  disposed  of. 

In  a  later  chapter  we  shall  have  more  to  say  of  the 
origin  and  function  of  hypotheses.  What  we  wish  to 
stress  just  now  is  the  activity  of  the  mind  in  every 
stage  of  investigation.  To  leave  out  the  mind  is  like 
removing  Hamlet  from  the  play. 

REFERENCES 

Dewey,  How  We  Think,  chap.  vii. 

James,  Principles  of  Psychology,  vol.  I,  p.  192/. 

Jevons,  Principles  of  Science,  vol.  I,  chap.  xv. 

Merz,  History  of  European  Thought,  vols.  I  and  il,  passim. 

Welton,  Manual  of  Logic,  vol.  ii,  chap.  vi. 


CHAPTER  XVII 

OBSERVATION  AND  FACT 

The  Need  of  Observation.  Since  the  principle 
which  should  control  all  investigation  is  fidelity  to  rele- 
vant fact,  we  must  emphasize  the  part  played  by  obser- 
vation. Mere  speculation  uncontrolled  by  fact  is  almost 
certain  to  lose  touch  with  reality.  It  may  lead  to  the 
construction  of  beautiful  systems  but  these  systems  for 
all  their  splendor  and  subtlety  are  sure  to  lack  value 
as  means  of  interpreting  the  world  in  which  we  actu- 
ally live.  True  systems  of  knowledge  must  be  given  a 
factual  foundation.  Fact  is  both  the  stimulus  to,  and 
the  test  of,  knowledge.  But  fact  can  be  obtained  only 
by  observation,  direct  or  indirect.  The  investigator 
must  either  gather  his  data  himself  or  else  trust  to  the 
testimony  of  others.  The  precept  which  the  logician 
feels  called  upon  to  enforce  is  that  the  observational 
side  of  investigations  should  be  thorough  and  unbiased. 
Only  in  this  way  can  data  approach  that  objectivity 
which  is  the  ideal  of  logical  thought. 

The  Difficulty  of  securing  Data.  The  sources  of 
knowledge,  so  far  as  facts  are  concerned,  gire  direct  and 
indirect.  The  only  direct  way  is  by  means  of  personal 
observation,  and  this  involves  perception.  Even  mem- 
ory must  be  regarded  as  an  indirect  source  since  mem- 
ory is  the  more  or  less  correct  revival  of  what  has  once 
been  experienced.  Another  motive  for  classifying  mem- 
ory among  the  indirect  sources  of  knowledge  is  the 


OBSERVATION  AND  FACT  185 

greater  danger  of  mistake.  Slight,  if  not  gross,  errors 
in  memory  are  so  frequent  that  careful  thinkers  feel 
compelled  to  take  the  greatest  precautions  and  to  insti- 
tute some  method  of  record  which  will  serve  as  a  sub- 
stitute for  the  details  which  are  so  easily  forgotten  or 
changed. 

Conditions  of  Accurate  Observation.  The  psy- 
chologist informs  us  that  we  notice  only  the  things 
which  interest  us.  Many  stimuli  come  to  our  senses 
which  never  pass  into  consciousness  because  they  do 
not  awaken  even  a  passing  attention.  This  control  of 
observation  by  interest  is  strikingly  exemplified  by  the 
different  accounts  of  events  given  by  eye-witnesses. 
The  records  of  the  law  courts  are  full  of  such  conflict- 
ing testimonies  on  the  part  of  eye-witnesses,  and  the 
experimental  psychologist  has  been  making  experi- 
ments to  study  the  degree  of  accuracy  to  be  expected. 
The  following  example  may  make  clearer  the  difficulty 
in  securing  trustworthy  data  when  the  series  of  events 
to  be  observed  is  complex :  "  A  few  years  ago  a  painful 
scene  occurred  in  Berlin,  in  the  University  Seminary 
of  Professor  von  Liszt,  the  famous  criminologist.  The 
Professor  had  spoken  about  a  book.  One  of  the  older 
students  suddenly  shouts,  'I  wanted  to  throw  light 
on  the  matter  from  the  standpoint  of  Christian  mor- 
ality I '  Another  student  throws  in,  '  I  cannot  stand 
that ! '  The  first  starts  up,  exclaiming,  '  You  have  in- 
sulted me ! '  The  second  clenches  his  fist  and  cries,  '  If 
you  say  another  word  — '  The  first  draws  a  revolver. 
The  second  rushes  madly  upon  him.  The  Professor 
steps  between  them  and,  as  he  grasps  the  man's  arm, 
the  revolver  goes  off.  General  uproar.  In  that  moment 


186  THE  ESSENTIALS  OF  LOGIC 

Professor  Liszt  secures  order  and  asks  a  part  of  the 
students  to  write  an  exact  account  of  all  that  has  hap- 
pened. The  whole  had  been  a  comedy,  carefully  planned 
and  rehearsed  by  the  three  actors  for  the  purpose  of 
studying  the  exactitude  of  observation  and  recollection. 
Those  who  did  not  write  the  report  at  once  were,  part 
of  them,  asked  to  write  it  the  next  day  or  a  week  later ; 
and  others  had  to  depose  their  observations  under  cross- 
examination.  The  whole  objective  performance  was  cut 
up  into  fourteen  little  parts  which  referred  partly  to 
actions,  partly  to  words.  As  mistakes  there  were  counted 
the  omissions,  the  wrong  additions,  and  the  alterations. 
The  smallest  number  of  mistakes  gave  twenty-six  per 
cent  of  erroneous  statements ;  the  largest  was  eighty  per 
cent.  The  reports  with  reference  to  the  second  half  of 
the  performance,  which  was  more  strongly  emotional, 
gave  an  average  of  fifteen  per  cent  more  mistakes  than 
those  of  the  first  half.  Words  were  put  into  the  mouths 
of  men  who  had  been  silent  spectators  during  the  whole 
short  episode ;  actions  were  attributed  to  the  chief  par- 
ticipants of  which  not  the  slightest  trace  existed ;  and 
essential  parts  of  the  tragi-comedy  were  completely 
eliminated  from  the  memory  of  a  number  of  witnesses."  * 
In  such  cases  there  is  hardly  such  a  thing  as  pure  per- 
ception. Suggestion,  imagination,  and  inference  shoot 
through  what  is  called  'perception.'  It  is  obvious 
that  it  is  not  very  easy  to  find  fact  even  when  we  wish 
to  be  faithful  to  it.  But  forewarned  is  at  least  fore- 
armed. 

In  physical  science  the  facts  to  observe  are  seldom 
as  complex  as  in  social  matters.  Yet  the  warning  is  not 
1  Miinsterberg,  On  the  Witness  Stand,  pp.  49-50. 


OBSERVATION  AND  FACT  187 

out  of  place  in  the  physical  field.  The  chief  advantage 
which  the  scientist  has  is  that  he  can  repeat  his  facts 
until  he  is  satisfied  that  he  has  them  correctly. 

Haphazard  observation  occurs  when  there  is  no  very 
definite  purpose  back  of  the  series  of  perceptions. 
Things  and  events  are  then  noted  at  random  according 
to  the  interests  and  associations  which  happen  to  come 
uppermost.  When  such  haphazard  observations  are  ex- 
amined, they  are  nearly  always  found  to  be  too  inac- 
curate or  fragmentary  to  be  of  much  value.  We  see, 
then,  that  one  of  the  prime  conditions  of  good  obser- 
vation is  dejiniteness  of  purpose.  The  investigator  must 
be  on  the  outlook  for  facts  of  a  known  character  or  he 
will  miss  them.  We  are  all  aware  that  we  are  more  apt 
to  find  a  lost  article  if  we  know  what  to  look  for.  The 
scientist  who  is  carrying  on  an  investigation  has  a 
fairly  definite  problem  in  mind  which  narrows  the  field 
of  attention.  This  is  one  of  the  reasons  why  experi- 
mentation is  so  satisfactory. 

Another  condition  of  good  observation  is  the  posses- 
sion of  good  mental  habits.  He  who  is  on  his  guard 
against  the  influences  constantly  at  work  to  distort  ob- 
servation is  more  apt  to  observe  correctly.  He  will  try 
to  keep  his  mind  open,  to  thrust  prejudices  and  pre- 
conceptions aside,  to  allow  facts  repugnant  to  him,  for 
one  reason  or  another,  as  much  weight  as  favorable  facts  ; 
in  short,  he  will  try  to  keep  his  mind  as  receptive  to  all 
relevant  facts  as  he  is  able.  This  neutrality  of  mind  is 
harder  to  attain  to  than  is  generally  supposed.  It  is  an 
achievement  of  training  and  education. 

Errors  in  Perception.  Errors  in  perception  are 
usually  classified  under  two  headings,  '  mal-observation ' 


188  THE  ESSENTIALS  OF  LOGIC 

and '  non-observation.'  Mal-observation  is,  again,  of  two 
kinds :  addition  to  what  is  present  and  wrong  arrange- 
ment of  the  parts.  Non-observation  is  essentially  omis- 
sion. Let  us  consider  these  types  of  perceptual  error 
in  some  detail. 

We  constantly  add  elements  to  interpret  or  enlarge 
what  we  actually  perceive.  This  is  not  surprising  when 
we  remember  that  sensation  is  only  a  small  part  of  per- 
ception. Association  and  suggestion  are  fundamental 
factors  in  perception,  and  we  see  what  we  wish  to  see 
or  expect  to  see  so  long  as  the  sense-factors  and  the 
general  situation  do  not  forbid  us.  When  common  sense 
says  that  seeing  is  believing,  it  is  not  aware  of  the  part 
played  by  past  experience  and  by  desire  in  what  we 
ordinarily  take  to  be  given.  And  this  ignorance  that 
perception  is  a  product  accounts  for  the  dogmatism  of 
common  sense  and  for  its  perplexity  when  confronted 
by  varying  stories  of  the  same  events.  In  his  book  en- 
titled On  the  Witness  Standi  Professor  Miinsterberg 
illustrates  the  influence  of  mental  factors  in  perception 
by  the  following  instances :  "  In  some  Bowery  wrangle, 
one  witness  was  quite  certain  a  rowdy  had  taken  a  beer- 
mug  and  kept  it  in  his  fist  while  he  beat  with  it  the 
skull  of  his  comrade ;  while  others  saw  that  the  two 
were  separated  by  a  long  table,  and  that  the  assailant 
used  the  mug  as  a  missile,  throwing  it  a  distance  of  six 
or  eight  feet.  In  another  trial,  one  witness  noticed  at 
the  seashore  in  moonlight  a  woman  with  a  child,  while 
another  witness  was  not  less  sure  that  it  was  a  man 
with  a  dog.  And  only  recently  passengers  in  a  train 
which  passed  a  courtyard  were  sure,  and  swore,  that 
they  had  taken  in  at  a  glance  the  distinct  picture  of  a 


OBSERVATION  AND  FACT  189 

man  whipping  a  child ;  one  swore  that  he  had  a  clean- 
shaven face,  a  hat,  and  was  standing,  while  another 
swore  that  he  had  a  full  beard,  no  hat,  and  was  sitting 
on  a  bencli.  The  other  day  two  most  reliable  expert 
shorthand  writers  felt  sure  that  they  heard  the  utterances 
which  they  wrote  down,  and  yet  the  records  differed 
widely  in  important  points." 

Non-observation  is  the  overlooking  of  facts  which 
ought  to  be  observed.  "It  is  exceeding  rare  to  find 
persons  who  can  with  perfect  fairness  estimate  and  reg- 
ister facts  for  and  against  their  own  peculiar  views  and 
theories.  Among  uncultivated  observers  the  tendency 
to  remark  favorable  and  forget  unfavorable  events  is 
so  great  that  no  reliance  can  be  placed  upon  their  sup- 
posed observations.  Thence  arises  the  enduring  fallacy 
that  the  changes  of  the  weather  coincide  in  some  way 
or  other  with  the  changes  of  the  moon,  although  exact 
and  impartial  registers  give  no  countenance  to  the  fact. 
The  whole  race  of  prophets  and  quacks  live  upon  the 
overwhelming  effect  of  one  success,  compared  with 
hundreds  of  failures  which  are  unmentioned  and  for- 
gotten. As  Bacon  says,  '  Men  mark  when  they  hit,  and 
never  mark  when  they  miss.'  We  should  do  well  to 
bear  in  mind  the  ancient  story,  quoted  by  Bacon,  of  one 
who  in  pagan  times  was  shown  a  temple  with  a  picture 
of  all  the  persons  who  had  been  saved  from  shipwreck, 
after  paying  their  vows.  When  asked  whether  he  did 
not  now  acknowledge  the  power  of  the  gods,  '  Aye,' 
he  answered,  '  but  where  are  they  painted  that  were 
drowned  after  their  vows ?  '" i 

Causes    of   Erroneous    Perception.     A  helpful 

'  Jevons,  The  Principles  of  Science,  vol.  Ii,  p.  6. 


190  THE  ESSENTIALS  OF  LOGIC 

classification  of  the  causes  of  erroneous  perception  is 
into  physical,  physiological,  and  psychological. 

Physical  conditions  are  very  important  for  correct 
observation.  When  the  atmosphere  is  unclear,  the  sci- 
entist does  not '  make  observations,'  for  he  knows  that  his 
data  will  be  faulty.  But  since  we  are  as  much  concerned 
with  everyday  reasoning  as  with  science,  we  must  note 
some  of  the  difficulties  due  to  external  conditions.  Ob- 
jects change  their  colors  according  to  the  source  of  illu- 
mination. In  a  fog,  objects  look  immense  because  our 
ordinary  standards  are  removed.  The  dweller  in  the  plain 
is  unable  for  a  long  time  to  estimate  distances  in  a 
mountainous  region  correctly.  On  the  more  technical 
side,  we  may  mention  the  fact  that  instruments  affect 
perception  in  various  ways.  Unless  these  sources  of 
change  are  recognized  and  met,  the  data  obtained  may 
be  misleading. 

Physiological  conditions  are  likewise  important. 
Taste  and  color  are  affected  by  the  condition  of  the 
body.  Again,  the  registration  of  flashes  of  light  in  their 
time-relations  cannot  be  made  by  perception  because  of 
a  certain  inertia  in  the  nervous  system.  A  glare  of 
light  is  necessarily  seen  some  fraction  of  a  second  after 
the  eye  has  been  stimulated.  In  delicate  scientific  work, 
the  part  played  by  the  organism  in  perception  is  taken 
account  of  and  automatic  registrations  are  employed 
wherever  possible. 

Psychological  factors  are  of  more  importance,  but, 
since  we  have  made  some  mention  of  them  already,  we 
will  not  dwell  upon  the  topic.  Misplaced  attention  leads 
to  faulty  observation.  This  cause  is  important  in  the 
activity  of  the  prestidigitator,  the  false  medium,  the 


OBSERVATION  AND  FACT  191 

pickpocket ;  they  direct  the  attention  of  their  subjects 
away  from  what  is  actually  of  most  importance  to 
them.  Another  instance  of  the  significance  of  the  psy- 
chological element  is  the  value  of  training  in  the  use 
of  instruments  such  as  the  microscope.  Again,  the  mind 
is  affected  by  bad  health.  There  is  not  the  same  possi- 
bility of  controlled  and  tireless  attention  under  abnor- 
mal conditions,  however  induced.  An  individual  must 
be  physically  and  mentally  fit  to  be  in  a  good  condition 
for  observation. 

Summary  for  Perception.  Seeing  is  not  the  sim- 
ple and  direct  operation  so  often  assumed.  It  has  its 
conditions,  physical,  physiological,  and  psychological. 
Of  these,  the  psychological  are  of  the  greatest  impor- 
tance for  everyday  life.  Association  and  past  experi- 
ence in  general  play  into  perception,  and  its  direction 
and  content  are  determined  by  interest,  desire,  and 
other  obscurer  factors.  Consequently,  perception,  even, 
cannot  be  taken  at  its  face  value  when  much  is  at 
stake ;  it  must  be  tested  and,  if  possible,  repeated.  We 
see  much  less  than  we  suppose,  and  that  is  why  obser- 
vation is  fullest  when  we  have  a  definite  purpose. 

Observation  in  Everyday  Life  and  in  Science. 
Because  the  scientist  has  become  aware  of  these  dangers, 
he  has  made  observation  a  more  careful  and  intelligent 
operation  than  it  is  in  everyday  life.  The  scientist 
makes  an  observation.  He  knows  what  he  is  about 
and  guards  against  dangers  so  far  as  possible.  One  ad- 
vantage he  usually  has  is  that  his  observations  can  be 
repeated.  An  individual  who  is  called  before  a  court 
as  a  witness  is  only  too  painfully  conscious  that  he  did 
not  know  just  what  to  observe ;  his  attention  was  too 


192  THE  ESSENTIALS  OF  LOGIC 

diffused  and  unguided  to  give  definite  results.  He  has, 
moreover,  no  records  and  must  trust  to  memory  with 
its  attendant  errors. 

Memory  and  Facts.  Memory  is  selective  much 
as  perception  is.  We  are  likely  to  remember  only 
those  events  which  we  have  expressly  attended  to ; 
and  a  further  elimination  comes  from  the  fact  that 
we  are  much  more  apt  to  remember  favorable  than  un- 
favorable things.  This  tendency  to  forget  what  is 
unpleasant  was  recognized  by  Darwin.  "I  had  also," 
he  writes,  "  during  many  years,  followed  a  golden  nde 
—  namely,  whenever  a  published  fact,  a  new  observa- 
tion or  thought  came  across  me,  which  was  opposed  to 
my  general  results,  to  make  a  memorandum  of  it  with- 
out fail  and  at  once  ;  for  I  had  found  hy  experience 
that  such  facts  and  thoughts  were  far  more  apt  to 
escape  from  the  memory  than  favorable  ones.  Owing 
to  this  habit,  very  few  objections  were  raised  against 
my  views  which  I  had  not  at  least  noticed  and  at- 
tempted to  answer."  ^ 

Habits  of  mind  or  customary  points  of  view  furnish 
the  centers  for  this  unconscious  selection.  Events  which 
cannot  be  made  to  fit  into  the  scheme  of  values  and 
ideas  which  is  gradually  established  in  the  personality 
drop  into  the  background  and  finally  cease  to  appear 
in  consciousness.  Not  only  is  there  omission,  there  is 
also  distortion  and  coloring  of  what  is  remembered. 
A  person  who  writes  his  autobiography  is  apt  to  dis- 
tort the  facts  of  his  life.  That  is  why  such  narra- 
tives must  always  be  checked  where  possible  by  ex- 
ternal evidence.  We  must  not  say  that  Wagner  and 
^  Avcloliography,  p.  87. 


OBSERVATION  AND  FACT  193 

Disraeli  lied,  they  simply  deceived  themselves.  Who, 
moreover,  can  be  perfectly  frank,  even  to  himself, 
about  himself?  Inhibitions  of  various  sorts  and  our 
dramatic  sense  are  at  work  upon  the  materials  of  our 
past  life  to  make  them  more  presentable. 

Summary  of  Causes  of  Mistaken  Memory.  The 
following  summary  of  the  causes  of  mistaken  memory 
may  be  helpful:  — 

We  tend  to  remember  what  has  usually  happened 
and  to  forget  the  exceptional  unless  it  is  very  striking. 

We  tend  to  remember  events  which  are  pleasant 
and  fit  in  with  the  general  trend  of  our  lives  and  the 
drift  of  our  ideas. 

We  tend  to  remember  the  heights  and  depths  and 
to  allow  the  more  colorless  events  to  lapse. 

We  tend  to  dramatize  and  develop  events  by  an  un- 
conscious process  of  construction  and  inference. 

The  logician  is  aware  that  memory  is  not  an  intui- 
tion but  a  product,  and  that  it  must  be  tested  by  its 
inner  consistency  and  by  means  of  external  evidence. 
The  shorter  the  time  which  has  elapsed,  the  more 
truthful  it  is  found  to  be. 

Testimony.  Testimony  is  a  still  more  indirect  source 
of  knowledge  than  memory.  When  we  ourselves  have 
not  been  the  witnesses  of  an  occurrence,  we  are  com- 
pelled to  have  recourse  to  the  statements  of  eye-wit- 
nesses. But  a  double  danger  of  error  is  now  present. 
We  must  be  certain  that  those  who  claim  to  be  were 
actually  witnesses  at  first  hand.  Even  so,  they  were  sub- 
ject to  all  the  causes  of  mal-observation  which  we  have 
already  stressed,  and,  added  to  this,  is  the  liability  to 
change  which  their  testimony  is  subject  to  in  its  passage 


194  THE  ESSENTIALS  OF  LOGIC 

to  our  minds.  Mal-observation,  fallacious  memory,  in- 
accurate expression,  misinterpretation,  this  is  the  series 
of  distorting  tendencies  which  makes  '  fact '  always 
more  or  less  hypothetical.  The  consequence  is  that 
such  tentative  facts  must  be  carefully  examined  before 
they  are  accepted.  Methodical  tests  must  be  worked 
out  and  carefully  applied;  it  is  not  too  much  to  say 
that  facts  are  critical  judgments  rather  than  something 
passively  given. 

Facts  differ  in  Different  Sciences.  The  data  to 
which  the  investigator  must  adhere  in  his  achievement 
of  systematic  knowledge  vary  from  science  to  science. 
It  is  very  important  to  bear  this  in  mind,  for,  other- 
wise, it  is  impossible  to  understand  differences  in  the 
methodology  and  technique  of  these  various  sciences. 
Inductive  logic  cannot  be  formal  to  the  same  extent 
that  the  logic  of  consistency  is  able  to  be.  The  geo- 
metrician secures  his  data  by  means  of  axioms  and 
postulates  which  seem  to  him  self-consistent,  and  which 
he  relates  to  a  spatial  system  lending  itself  to  construc- 
tion dnd  manipulation.  His  methods  reflect  this  founda- 
tion and  are  dominantly  inspectional  and  deductive. 
The  physical  sciences  obtain  their  data  by  active  ob- 
servation aided  by  experimentation.  These  observations 
lend  themselves  to  repetition.  The  historical  and  social 
sciences  have  more  difficulty  in  securing  their  data ;  in 
fact,  data  are  more  the  end-terms  of  their  investiga- 
tions than  the  beginning.  In  their  cases,  we  must  dis- 
tinguish between  the  crude  material  with  which  they 
start  and  the  conclusions  upon  which  they  base  their 
final  interpretations.  Between  these  stages  lies  a  per- 
fected technique  of  criticism  and  analysis.    Thus  the 


OBSERVATION  AND  FACT  195 

character  of  investigation  is  modified  by  the  nature  of 
the  problem,  the  aim  of  the  investigator,  and  the  kind 
of  knowledge  achieved.  In  spite  of  this  variation,  there 
is,  however,  the  constant  presence  of  the  three  elements 
to  which  we  referred  in  the  chapter  introductory  to 
this  part  of  logic.  There  must  be  observation  and  col- 
lection of  data,  conjecture,  systematic  reasoning  about 
the  conjecture,  and,  finally,  a  return  to  observation. 
Only  as  the  result  of  such  systematic  inference  can 
knowledge  be  achieved. 

What  are  Relevant  Facts?  We  speak  of  the 
facts  of  a  case  and  of  relevant  facts ;  how  do  we  know 
what  facts  are  relevant  and  what  facts  do  actually  be- 
long to  the  case  ?  They  do  not  come  labeled  nor  is  the 
degree  of  their  importance  visibly  stamped  upon  them. 
A  prime  condition  of  the  acquisition  of  essential  facts 
is  guidance  by  some  idea.  We  must  know  what  we 
want,  must  have  insight,  judgment,  discernment.  Such 
discernment  is,  in  part,  the  effect  of  familiarity  with 
the  field.  The  expert  knows  what  to  look  for ;  he  is 
able  to  narrow  down  the  search  to  data  of  a  certain 
character.  There  is  in  this  sense  of  location  what  the 
psychologist  calls  an  apperceptive  or  deductive  element. 
Past  experience  is  funded.  We  see  and  judge  with  the 
mind.  Strictly  speaking,  there  is  no  such  thing  as 
purely  passive  observation.  There  is  usually  a  decid- 
edly purposive  factor  at  work.  Guesses  and  conjectures 
arise  to  guide  the  direction  in  which  to  look  for  evi- 
dence. Especially  is  this  the  case  when  resort  is  had 
to  experimentation.  We  may  say,  then,  that  all  obser- 
vation involves  the  selection  of  what  is  thought  to  be 
essential.  The  mind  picks  from  the  crowd  of  facts  press- 


M6  THE  ESSENTIALS  OF  LOGIC 

ing  upon  attention  those  which  are  judged  to  be  rele- 
vant. In  other  words,  observation  is  in  the  service  of  a 
continuous  process  of  interpretation  and  judgment. 


REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  xm. 
Gibson,  The  Problem  of  Logic,  chap.  xin. 
Jevons,  Lessons  in  Logic,  chap.  xxvn. 
Jones,  Logic,  Inductive  and  Deductive,  chap.  n. 
Sidgwick,  The  Process  of  Argument,  chap.  VUL 


CHAPTER  XVIII 

THE  ORIGIN  AND  USE  OF  HYPOTHESES 

"What  is  an  Hypothesis  ?  An  hypothesis  is  any 
conception  by  which  the  mind  goes  beyond  the  known 
facts  and  seeks  to  establish  relations  between  data  of 
testimony  and  perception^  so  long  as  that  conception 
is  one  among  alternative  possibilities  and  is  not  con- 
sidered a  fact.  This  definition,  adapted  from  Bosan- 
quet's  larger  Logic^  brings  out  the  essential  position  of 
an  hypothesis  as  between  accepted  fact  and  accepted 
theory.  It  is  a  conjecture,  a  guess,  a  provisional  expla- 
nation. Just  because  an  hypothesis  is  conjectural,  it  is 
primarily  a  mental  contribution  whose  aim  is  the  solu- 
tion of  some  problem.  It  is  an  interpretation  or  en- 
largement of  what  is  given. 

As  a  tentative  solution  of  a  problem,  an  hypothesis 
is  an  idea  held  before  the  mind  in  answer  to  a  purpose, 
that  of  explanation.  But  this  purpose  cannot  be  ful- 
filled until  many  further  steps  are  taken.  The  implica- 
tions of  the  conjecture  must  be  reasoned  out  and  the 
attempt  made  to  bring  them  into  touch  with  a  com- 
pleter survey  of  the  facts.  Hence,  a  genuine  hypothesis 
arises  in  fact  and  keeps  in  touch  with  fact  throughout 
its  history.  Because  of  this  continuous  responsibility 
to,  and  control  by,  fact,  the  conjectural  stage  in  inves- 
tigation does  not  sin  against  the  inductive  principle  of 
Fidelity  to  Fact.  All  that  must  be  guarded  against  is 
that  dreamy  sort  of  speculation  which  soars  into  the 


198  THE  ESSENTIALS  OF  LOGIC 

heavens  and  never  seeks  to  return.  "  The  truly  scien- 
tific thinker  has  none  of  the  spirit  which  says,  '  If  the 
facts  do  not  agree  with  the  theory,  so  much  the  worse 
for  the  facts.'  "  i 

Kinds  of  Hypotheses.  The  nature  of  a  particular 
hypothesis  depends  upon  the  character  of  the  problem 
for  which  it  is  a  tentative  answer.  Sometimes  we  are 
on  the  lookout  for  a  fact,  as  when  we  are  in  search  for 
a  particular  cause  of  an  occurrence  like  a  fire  or  a 
crime ;  sometimes  we  wish  to  establish  a  law  of  nature, 
such  as  a  law  of  physical  chemistry ;  sometimes  we  de- 
sire to  conceive  the  structure  of  an  empirical  substance 
like  rubber  or  protoplasm ;  sometimes  we  are  pressing 
forward  to  some  immense  generalization  like  the  prin- 
ciple of  the  conservation  of  energy  or  the  theory  of 
evolution.  In  each  case,  the  mind  must  suggest  ideas 
and  then  seek  to  establish  them.  The  nature  of  the 
problem  determines  the  character  of  the  explanatory 
conjecture. 

Are  Hypotheses  necessary  for  Science?  At 
various  times  in  its  history,  science  has  been  skeptical 
of  the  necessity  and  even  of  the  value  of  hypotheses. 
During  such  periods,  the  ideal  is  to  let  facts  speak  for 
themselves.  It  is  supposed  that,  if  facts  enough  are 
collected  and  tabulated,  the  principle  which  is  sought 
will  somehow  stand  out  from  them  and  force  itself  on 
the  attention.  "  The  natural  goal  of  science  based  on 
this  radically  empirical  method  is  to  become  a  Science 
of  Statistics  so  compiled  and  arranged  as  to  force  upon 
the  methodical  collector  of  observations  the  laws  which 
the  facts  require  to  explain  them.  In  this  way,  labori- 
^  Welton,  Manual  of  Logic,  vol.  u,  p.  86. 


THE  ORIGIN  AND  USE  OF  HYPOTHESES     199 

ous  method  takes  the  place  of  the  scientific  imagination 
and  the  happy  idea."  ^  This  way  of  approach  is  often 
called  the  *  Baconian  method '  after  Francis  Bacon,  one 
of  the  founders  of  modern  logic.  It  represents  a  pro- 
test against  an  overspeculative  tendency  not  fed  on 
facts.  It  is,  however,  itself  obviously  another  extreme. 
The  relative  importance  of  theory  and  fact  varies  from 
time  to  time  and  from  subject  to  subject.  It  is  now 
pretty  generally  held  that  the  situation  controls  the 
amount  of  conjecture,  but  that  a  free  play  of  the  mind 
must  always  be  present.  It  is  psychologically  impos- 
sible for  principles  to  arise  from  facts  without  the  col- 
laboration of  the  mind.  Neither  observation  nor  concep- 
tion is  a  passive  event.  Science  is  not  a  mere  collection 
of  facts. 

A  brilliant  group  of  men  who  were  at  once  scientists 
of  recognized  rank  and  thinkers  championed  the  cause 
of  hypotheses  during  the  latter  part  of  the  nineteenth 
century,  and  their  vindication  of  the  controlled  use  of 
hypotheses  has  won  general  acceptance.  These  men 
worked  in  both  the  physical  and  the  biological  sciences. 
The  following  quotation  from  Huxley  is  typical :  "  It 
is  a  favorite  popular  delusion  that  the  scientific  inquirer 
is  under  a  sort  of  moral  obligation  to  abstain  from  going 
beyond  that  generalization  of  observed  facts  which  is 
absurdly  called '  Baconian '  induction.  But  any  one  who 
is  practically  acquainted  with  scientific  work  is  aware 
that  those  who  refuse  to  go  beyond  fact  rarely  get  as  far 
as  fact ;  and  any  one  who  has  studied  the  history  of  science 
knows  that  almost  every  great  step  therein  has  been 
made  by  *  anticipation  of  nature,'  that  is,  by  the  inven- 

^  Gibson,  The  Problem  of  Logic,  p.  313. 


200  THE  ESSENTIALS  OF  LOGIC 

tion  of  hypotheses  which,  though  verifiable,  often  had 
little  foundation  to  start  with,  and  not  infrequently,  in 
spite  of  a  long  career  of  usefulness,  turned  out  to  be 
wholly  erroneous  in  the  long  run."  ^ 

The  Origin  of  Hypotheses.  There  are  at  least  two 
conditions  leading  to  the  formation  of  hypotheses,  the 
possession  of  facts  bearing  upon  a  problem  and  mental 
spontaneity.  There  is  a  constant  interaction  between 
these  two  factors  the  one  creative  and  the  other  con- 
trolling and  suggestive.  As  a  rule,  an  hypothesis  is  not 
a  sudden  intuition,  but  a  mental  growth  which  matures 
in  the  fertile  soil  of  accurate  and  extensive  knowledge. 
When  the  history  of  any  progressive  investigation  is 
written,  analysis  shows  that  there  is  a  continuous  trans- 
verse movement  between  data  and  conjecture.  Conjecture 
guides  observation  and  experimentation  while  the  results 
of  such  further  observation  modify  conjectures  and  se- 
lect among  them.  We  must  always  remember  that  the 
steps  of  induction  which  the  logician  separates  out  for 
study  do  not  exist  separately  as  mutually  exclusive  stages. 

There  is  pretty  general  agreement  that  fruitful  hy- 
potheses are  creations  of  constructive  imagination.  In 
its  higher  levels,  such  constructive  imagination  is  a  rare 
gift.  A  great  scientist  must  combine  many  capacities ; 
he  must  be  a  tireless  observer  and  classifier ;  he  must 
be  able  to  organize  his  material  and  include  it  in  one 
comprehensive  survey ;  but  he  must  also  be  able  to  seize 
that  idea  which  will  illuminate  it  and  give  it  life  and 
meaning.  Tyndall  was  aware  of  the  importance  of  this 
more  personal  factor  of  imaginative  interpretation  when 
he  wrote :  "  With  accurate  experiment  and  observation 
1  Methods  and  ResultB,  p.  62. 


THE  ORIGIN  AND  USE  OF  HYPOTHESES     201 

to  work  upon,  Imagination  becomes  the  architect  of 
physical  theory.  Newton's  passage  from  a  falling  apple 
to  a  falling  moon  was  an  act  of  the  prepared  imagina- 
tion, without  which  the  'laws  of  Kepler'  could  never 
have  been  traced  to  their  foundations.  Out  of  the  facts 
of  chemistry  the  constructive  imagination  of  Dalton 
formed  the  atomic  theory.  Davy  was  richly  endowed 
with  the  imaginative  faculty,  while  with  Faraday  its 
exercise  was  incessant,  preceding^  accompanying,  and 
guiding  all  his  experiments.  His  strength  and  fertility 
as  a  discoverer  is  to  be  referred  in  great  part  to  the 
stimulus  of  his  imagination.  Scientific  men  fight  shy  of 
the  word  because  of  its  ultra-scientific  connotations ;  but 
the  fact  is,  that,  without  the  exercise  of  this  power,  our 
knowledge  of  nature  would  be  a  mere  tabulation  of  co- 
existences and  sequences."  ^ 

A  Grlance  at  the  Psychology  of  Conjecture.  The 
form  of  scientific  imagination  varies  with  the  nature  of 
the  science.  "  No  one  will  question  that  mathematicians 
have  a  way  of  thinking  all  their  own ;  but  even  this  is  too 
general.  The  arithmetician,  the  algebraist,  and  more 
generally  the  analyst,  in  whom  invention  obtains  in  the 
most  abstract  form  of  discontinuous  functions — sym- 
bols and  their  relations  —  cannot  imagine  like  the 
geometrician."  ^  The  case  seems  to  be  that  the  nature 
of  the  materials  is  a  factor  of  first  importance ;  it  is  deter- 
mining, and  indicates  to  the  mind  the  direction  in  which 
it  is  turned.  Furthermore,  some  individuals  are  better 
able,  by  the  very  constitution  of  their  minds,  to  work 
in  a  certain  kind  of  material  than  in  other  kinds.  Again, 

^  Fragments  of  Science,  pp.  111-12. 

'  Ribot,  Essay  on  the  Creative  Imagination,  p.  237. 


fm  THE  ESSENTIALS  OF  LOGIC 

there  are  distinct  differences  in  type  when  we  come  to 
consider  the  way  in  which  the  illuminating  idea  arrives. 
Roughly  speaking,  there  are  two  types  of  creative  minds, 
the  intuitive  and  the  reflective. 

With  the  intuitive  mind,  the  preparation  is  largely 
unconscious.  The  illuminating  idea,  when  it  does  come, 
seems  to  burst  upon  the  individual  hke  a  stroke  of  in- 
spiration. There  is  a  cry  of  '  Eureka '  and  the  new  view 
is  born.  Musicians  and  poets  are  more  likely  to  have  this 
type  of  creative  imagination  than  are  scientists;  yet 
*'Hauy  drops  a  bit  of  crystallized  calcium  spar,  and, 
looking  at  one  of  the  broken  prisms,  cries  out,  '  All  is 
found ! '  and  immediately  verifies  his  quick  intuition  in 
regard  to  the  nature  of  crystallization."  ^ 

The  reflective  mind,  on  the  other  hand,  realizes  that 
there  is  a  problem  to  solve  and  approaches  its  solution 
systematically.  Such  an  individual  gathers  his  material 
and  broods  over  it.  An  interpretative  idea  gradually 
forms  itself  and  is  developed  little  by  little.  Perhaps  it 
is  soon  rejected,  and  another  grows  up  to  supply  its 
place.  Kepler  is  a  good  example  of  the  reflective  mind. 
He  devoted  a  large  part  of  his  life  to  trying  new  and 
strange  hypotheses  about  the  planetary  movements  until 
the  day  he  discovered  the  elliptical  orbit  of  Mars. 

According  to  Ribot,  the  differences  between  these 
two  types  of  minds  are  largely  reducible  to  temperament 
and  disposition.  He  works  out  the  contrast  as  follows :  — 

Intuitive  type  Reflective  type 

Ready-witted  minds,  excelling  in  Logically  developing    minds, 
conception,  making  the  whole         excelling  in  elaboration, 
almost  out  of  one  piece. 

^  Bibot,  Essay  on  the  Creative  Imagination,  p.  247. 


THE  ORIGIN  AND  USE  OF  HYPOTHESES    203 

Intuitive  type  Reflective  type 

Work  primarily  unconscious.  Patience    the    preponderating 

role. 
Work  primarily  conscious. 
Actions  quick.  Actions  slow. 

When  we  contrast  these  two  types  of  mind,  it  be- 
comes evident  that  logic  has  more  to  learn  from,  and 
more  to  convey  to,  the  reflective  type.  But  we  must  not 
forget  that  in  any  complex  field  of  investigation  to-day, 
the  contrast  is  quite  relative.  There  must  always  be 
patience  and  conscious  effort. 

Running  all  through  logic  is  an  almost  moral  ele- 
ment. The  history  of  investigation  proves  that  certain 
attitudes  are  favorable  to  invention  and  discovery  while 
others  are  distinctly  unfavorable.  Creative  imagination 
does  not  exist  in  a  mind  that  is  conventional  and  domi- 
nated by  habit  and  routine.  "  Alertness,  flexibility,  cu- 
riosity, are  the  essentials ;  dogmatism,  rigidity,  prejudice, 
caprice,  arising  from  routine,  passion,  and  flippancy 
are  fatal."  ^ 

The  Value  of  Hypotheses.  We  have  already  said 
enough  to  indicate  wherein  the  value  of  an  hypothesis 
lies.  It  sharpens  and  guides  the  mental  eye.  The  fol- 
lowing anecdote  from  the  life  of  Darwin  brings  out  this 
feature  very  well :  "  Darwin  tells  of  a  geological  trip 
through  Wales  which  he  took  while  a  student  at  Cam- 
bridge, in  company  with  Sedgwick,  the  professor  of 
geology.  It  must  be  remembered  that  this  was  before 
Agassiz  had  come  forward  with  his  theory  of  a  glacial 
period  in  the  world's  history.  Darwin  writes :  '  We 
spent  many  hours  in  Cwm  Idwal,  examining  all  the 
»  Dewey,  How  We  Think,  pp.  105-06. 


204  THE  ESSENTIALS  OF  LOGIC 

rocks  with  supreme  care,  as  Sedgwick  was  anxious  to 
find  fossils  in  them ;  but  neither  of  us  saw  a  trace  of 
the  wonderful  glacial  phenomena  all  around  us  ;  we  did 
not  notice  the  plainly  scored  rocks,  the  perched  bould- 
ers, the  lateral  and  terminal  moraines.  Yet  the  phe- 
nomena are  so  conspicuous  that,  as  I  declared  in  a  paper 
published  many  years  afterward  in  the  Philosophical 
Magazine^  a  house  burnt  down  by  fire  did  not  tell  its 
story  more  plainly  than  did  this  valley.  If  it  had  been 
filled  by  a  glacier,  the  phenomena  would  have  been  less 
distinct  than  they  are  now.'  "  ^  As  James  put  it,  "  The 
only  things  which  we  commonly  see  are  those  which  we 
pre-perceive." 

But  an  hypothesis  is  of  value  also  because  it  begins 
a  systematic  analysis  and  synthesis  of  the  facts.  It  is 
the  beginning  of  an  explanatory  view  which  seeks  to 
penetrate  below  appearances  to  the  causes  at  work  and 
their  structure.  When  verified,  hypotheses  become  the- 
ories and  so  enter  as  substantial  elements  in  our  knowl- 
edge of  the  world. 

It  is  now  generally  admitted  that  an  hypothesis 
which  afterwards  turns  out  to  be  false  may  have  justi- 
fied itself  in  a  measure  by  its  serviceableness.  It  is  a 
nice  question  whether  this  relative  serviceableness  can 
be  connected  with  an  element  of  truth  in  its  constitu- 
tion or  whether  it  is  due  to  the  guidance  which  it  exer- 
cises. Any  conjecture  exerts  a  steadying  control  on 
attention  and  encourages  the  collection  of  facts,  some 
of  which  may  lead  to  its  own  dethronement.  We  must 
not  forget,  however,  that  an  accepted  hypothesis  may 
prevent  the  consideration  of  truer  ones  and  may  in 
*  Life  and  Lettera  of  Charles  Darwin,  quoted  from  Creighton. 


THE  ORIGIN  AND  USE  OF  HYPOTHESES     205 

this  way  retard  progress.  Certainly  it  is  better  to  deal 
with  true  hypotheses  than  with  erroneous  ones.  The 
Ptolemaic  Hypothesis  and  the  Newtonian  Corpuscular 
Theory  of  Light  are  famous  examples  of  long  accepted 
hypotheses  which  were  finally  rejected. 

The  danger  in  the  use  of  hypotheses  is  due  to  the 
tendency  to  dogmatism.  All  scientists  are  liable  to 
"  the  partiality  of  intellectual  parentage."  One  way  to 
counteract  this  latent  dogmatism  which  blinds  the  men- 
tal vision  is  to  become  conversant  with  the  history  of 
the  various  sciences.  When  we  see  theory  succeed  the- 
ory and  even  those  which  have  stood  the  acid  test  of 
years  of  investigation  modified  in  more  or  less  essential 
points,  we  are  less  apt  to  retain  our  primitive  assertive- 
ness.  Another  way  to  prevent  dogmatism  is  to  keep 
before  the  mind  at  one  and  the  same  time  a  number  of 
rival  hypotheses.  This  is  called  the  '  Method  of  Multiple 
Working  Hypotheses.' 

The  Development  of  an  Hypothesis.  An  hy- 
pothesis is  barren  which  cannot  be  so  developed  as  to 
imply  verifiable  consequences.  The  development  of  an 
hypothesis  is  sometimes  called  '  reasoning,'  sometimes 
'  deduction.'  What  we  do  is  to  work  out  its  conse- 
quences in  the  light  of  our  knowledge  of  the  system  in- 
volved. Ideas  which  at  first  glance  seemed  plausible 
frequently  turn  out  to  be  quite  impossible.  This  maul- 
ing-over  of  ideas  to  get  their  bearings  is  essential.  Let 
me  first  take  a  very  simple  case  to  illustrate  the 
method.  I  see  footprints  on  the  beds  in  the  garden 
which  I  have  just  planted.  The  idea  comes  to  me  that 
my  young  son  has  been  disobeying  my  injunctions.  But 
if  these  are  his  footprints,  they  will  be  only  so  large.  I 


206  THE  ESSENTIALS  OF  LOGIC 

look  more  closely  and  discover  that  they  are  larger. 
Thus  my  hypothesis  has  been  developed  and  tested. 
This  same  process  is  apparent  in  all  cases  of  reasoning. 
Detective  stories  are  full  of  rather  artificial  examples 
of  developed  guesses  which  are  valid  or  invalid  as  the 
case  may  be. 

Science  is  replete  with  hypotheses  which  have  lent 
themselves  to  development.  Thus,  Torricelli's  theory 
that  the  air  has  weight  implied  that  heavier  liquids 
would  not  be  raised  so  high  in  a  vacuum  as  lighter 
liquids.  This  implication  was  tested  and  found  to  hold. 
Another  implication  was  that  the  mercury  would  not 
stand  so  high  on  a  mountain  as  on  a  plain.  This  also  was 
verified.  The  implications  of  an  idea  can  often  be  worked 
out  only  by  one  who  is  cognizant  with  the  whole  system 
of  relations  and  facts  within  which  the  idea  must  fit. 
Thus,  Foucault  showed  that  it  takes  longer  for  light  to 
travel  in  a  dense  medium  than  in  a  rare  medium.  But 
the  Corpuscular  Theory  of  Newton  had  the  reverse  of 
this  for  its  implication,  and  was  therefore  disproved. 
The  general  form  of  reasoning  about  an  idea  is  hypo- 
thetical :  if  this  is  so,  then  this  other  is  so ;  but  if  this 
other  is  so,  then  this  fact  follows.  The  chain  may  be 
short  or  long,  but  it  must  eventually  end  in  a  datum 
theoretically  open  to  observation. 

The  Proof  of  an  Hypothesis.  A  distinction  must 
be  made  between  verifying  an  hypothesis  and  proving 
it.  An  hypothesis  is  verified  so  far  as  its  logical  conse- 
quences in  the  system  of  knowledge  of  which  it  claims 
to  be  part  are  harmonious  with  the  facts.  '  If  -4  is  B^ 
we  may  decide,  '  then  C  is  Z).'  We  observe  with  or 
without  experimentation  and   discover  that   C  is  D. 


THE  ORIGIN  AND  USE  OF  HYPOTHESES    207 

This  agreement  reinforces  our  inclination  for  the  posi- 
tion that  A  is  B.  So  long  as  there  is  no  other  claimant, 
we  tend  to  regard  the  conjecture  as  true.  It  cannot^ 
however^  be  said  to  be  proved  in  any  final  sense  until 
it  can  be  shown  that  no  other  hypothesis  can  account 
for  the  facts.  The  logical  situation  involves  the  princi- 
ple of  the  hypothetical  syllogism.  It  will  be  remem- 
bered that  it  is  impossible  to  affirm  the  consequent  and 
draw  a  certainly  valid  conclusion.  Because  C  is  Z),  it 
does  not  follow  that  A  is  B.  But  it  is  impossible  to 
eliminate  all  other  possible  theories  because  we  can 
never  be  certain  of  working  within  a  complete  disjunc- 
tion. What,  then,  determines  our  confidence  in  a  suc- 
cessful hypothesis  ?  Ultimately  a  consilience  of  results. 
When  a  very  large  field  is  covered  and  coordinated  by 
a  conjecture  and  no  other  plausible  idea  is  in  sight  or 
seems  likely  to  be  advanced,  we  give  our  assent  and 
regard  the  hypothesis  as  proved. 

Fact,  Theory,  and  Hypothesis.  Facts  are  of  two 
kinds,  facts  of  observation  and  facts  of  belief.  While 
it  must  not  be  forgotten  that  even  facts  of  observation 
are  really  statements  which  are  open  to  reasonable 
doubt,  the  judgments  and  tests  involved  are  usually 
simpler  than  for  the  second  kind  of  facts.  This  second 
class  of  facts  are  complex  statements  which  have 
reached  the  stage  of  practical  certainty.  They  are  far- 
ther away  from  perception  than  the  first  and  involve 
conceptual  construction  of  an  advanced  degree.  It  is  a 
fact  of  observation  that  a  stick  seems  bent  in  the  water, 
but  a  fact  of  assent  that  the  earth  revolves  around  the 
sun.  Both  classes  have  this  in  common  that  we  give 
their  members  whole-hearted  belief. 


208  THE  ESSENTIALS  OF  LOGIC 

When  an  idea  is  first  suggested  and  entertained  by 
the  mind,  it  is  called  an  '  hypothesis.'  When  its  conse- 
quences are  deduced  and  verified,  it  is  apt  to  be  digni- 
fied by  the  name  of  '  theory.'  When  it  has  gained  un- 
questioned acceptance,  it  is  likely  to  be  spoken  of  as  a 
'  fact '  or  a  *  principle.'  Not  so  long  ago,  evolution  was 
referred  to  as  an  hypothesis ;  then  it  became  a  theory ; 
now  it  has  attained  the  standing  of  a  fact  or  a  princi- 
ple. We  must  remember  that  there  is  no  court  of  adju- 
dication, so  that  what  is  a  principle  to  one  may  be  an 
hypothesis  to  another. 

Analogy  as  a  Basis  of  Reasoning.  The  remark 
is  often  made  that  such-and-such  a  conclusion  was 
reached  by  analogy.  We  admittedly  reason  hy  analogy 
from  one  field  to  another.  Examining  such  reasoning, 
logicians  point  out  that  it  consists  of  the  passage  from 
one  thing  or  group  of  things  to  another  because  of  a 
recognized  resemblance  between  them.  "  Two  things 
resemble  each  other  in  one  or  more  respects ;  a  certain 
proposition  is  true  of  one,  therefore  it  is  true  of  the 
other."  1  Now  such  a  passage  is  usually  tentative  and 
is  therefore  of  the  nature  of  an  hypothesis ;  this  fact  is 
our  justification  for  treating  the  topic  in  this  chapter. 

The  symbolic  form  of  analogy  is  as  follows :  A  re- 
sembles B  in  certain  respects ;  A  exhibits  the  charac- 
ter Fi  therefore  B  will  exhibit  the  character  T^also.  In 
other  words,  we  tend  to  hold  that  if  two  things  agree  in 
certain  respects  they  are  apt  to  agree  in  others.  All 
classification  is  really  based  on  analogy  in  this  broad 
sense;  but  in  classification  the  similarities  noted  are 
many  and  fundamental  and  we  are  dealing  with  what 
1  Mill,  System  of  Logic,  bk.  m,  chap,  zx,  par.  2. 


THE  ORIGIN  AND  USE  OF  HYPOTHESES    209 

we  have  reason  to  believe  are  things  of  the  same  kind. 
There  is,  however,  no  decided  break  between  what  is 
clearly  classification  and  what  would  be  admitted  by  all 
to  be  mere  analogy.  "  Where  analogy  is  very  close,  and 
well  tested,  and  familiar,  as  between  cancer  and  cancer, 
or  man  and  man,  class-names  have  generally  been  in- 
vented. It  is  newly  seen  likeness,  doubtful  likeness,  or 
likeness  where  the  examples  are  rare,  that  we  have  to 
recognize  as  well  as  we  can  without  the  aid  of  class- 
names.  And  it  is  to  these  kinds  of  likeness  especially 
that,  as  a  rule,  we  give  the  name  '  analogy.'  "  ^  It  is 
not  too  much  to  say  that  all  the  reasoning  in  a  new 
field  bases  itself  upon  analogies  with  more  familiar  do- 
mains. Thus  the  wave  character  of  the  propagation  of 
light  was  inferred  from  the  known  fact  that  sound 
which  also  was  reflected  traveled  in  waves. 

False  Analogy.  Analogies  are  very  apt  to  be  mis- 
leading. After  all,  things  may  be  similar  in  this  respect 
or  that  while  differing  in  almost  everything  else.  The 
points  of  similarity  are  often  superficial  and  not  corre- 
lated with  the  properties  which  are  important  for  the 
problem  in  hand.  Because  a  whale  lives  in  the  water 
and  is  shaped  very  much  like  a  fish,  it  does  not  follow 
—  as  was  at  one  time  supposed  —  that  it  has  the  deeper 
structure  of  a  fish.  Because  a  municipality  is  a  gov- 
ernment, it  does  not  follow  that  it  must  have  the  same 
type  of  organization  as  the  Federal  Government.  An 
argument  from  analogy  has  a  high  degree  of  probabil- 
ity only  when  the  points  of  resemblance  are  rooted  deep 
in  the  nature  of  the  two  things  and  there  is  reason  to 
believe  that  in  the  familiar  field  there  is  a  connection 

1  Sidgwick,  TJie  Process  of  Argument,  p.  40. 


210  THE  ESSENTIALS  OF  LOGIC 

between  the  points  of  resemblance  and  the  property 
which  we  wish  to  infer  in  the  new  field.  A  good  in- 
stance of  what  must  be  regarded  as  a  false  analogy  is 
Carlyle's  argument  against  the  representative  form  of 
government.  "  According  to  Carlyle,  this  kind  of  gov- 
ernment is  bound  to  fail,  since,  as  he  puts  it,  a  ship 
could  never  be  taken  around  Cape  Horn  if  the  captain 
were  obliged  to  consult  the  crew  every  time  before 
changing  his  course.  A  generalization  is  implied,  some- 
thing like,  '  The  sharing  of  power  involves  a  lack  of 
efficiency.'  Granted  that  this  holds  true  on  ships,  is  it 
also  true  in  government  ?  The  argument  asserts  that 
the  two  cases  are  alike,  but  it  offers  no  proof  that  the 
difference  in  circumstances  is  immaterial.  The  appar- 
ent difference,  however,  is  so  great  that  caution  is  ad- 
visable. It  may  be  that  the  lack  of  efficiency  is  due  to 
the  sharing  of  power  under  certain  conditions  peculiar 
to  the  management  of  ships."  ^ 

It  is  obvious  that  analogy  must  be  controlled  by  anal- 
ysis. False  analogies  always  rest  upon  the  disregard  of 
differences.  Thus  analogy  is  a  fruitful  source  of  sug- 
gestions but  these  must  be  tested  by  a  further  survey 
of  the  facts  and  an  estimation  of  their  meaning.  Re- 
semblance may,  as  the  saying  goes,  be  only  skin  deep. 

REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  XI. 
Joseph,  An  Introduction  to  Logic,  chap.  xxrv. 
Ribot,  Essay  on  the  Creative  Imagination,  chap.  IV. 
Sidgwick,  The  Process  of  Argument,  chap.  iv. 
Welton,  Manual  of  Logic,  vol.  n,  chaps,  in  and  rv. 

1  Bode,  An  Outline  of  Logic,  p.  163. 


CHAPTER  XIX 

THE  DISCOVERY  AND  PROOF  OP  CAUSAL  RELATIONS 

Ho-w  Experience  comes  to  us.  The  individual's 
experience  comes  to  him  in  an  accidental,  haphazard 
way,  and  it  is  only  as  the  result  of  unconscious  or 
semiconscious  sorting  and  generalization  that  he  re- 
duces it  to  some  show  of  order.  Things  are  recognized 
and  classified  into  kinds,  and  these  kinds  are  supposed 
to  have  certain  properties  which  can  be  predicted 
and  counted  on.  Iron  is  malleable  ;  coal  bums ;  swans 
are  white;  apple  trees  yield  apples  after  their  kind, 
etc.  By  means  of  these  classifications  and  generaliza- 
tions, we  are  able  to  handle  things  and  adapt  ourselves 
to  our  environment. 

But  there  is  another  feature  of  our  experience  which 
is  equally  important.  We  soon  learn  to  note  that 
events  in  which  we  are  interested  are  controlled  by 
conditions.  If  we  want  B  to  happen,  we  must  see  that 
A  is  added.  If  we  want  the  garden  to  produce  an 
abundant  crop,  we  must  add  fertilizer  in  the  proper 
proportions.  If  the  manufacturer  wishes  to  have  steel 
of  a  certain  degree  of  hardness,  he  must  add  manga- 
nese. When  any  factor  is  known  to  he  an  invariable 
antecedent  of  some  event  or  situation,  and  it  is  also 
known  that  this  event  does  not  occur  in  the  absence  of 
this  factor,  it  is  called  a  cause.  Such  a  cause  is  a 
means  to  an  end,  and  is  of  practical  significance.  If 
we  wish  to  achieve  any  result,  we  must  see  that  all  the 
conditions  are  present. 


212  THE  ESSENTIALS  OF  LOGIC 

What  are  Causal  Connections  ?  It  is  usually 
said  that  science  deals  with  the  causes  of  things.  What 
is  meant  by  this  expression  ?  And  what  is  a  cause  ?  A 
little  reflection  warns  us  that,  because  we  are  studying 
the  actual  methods  of  science,  we  have  to  do  with  a 
purely  empirical  problem.  What  the  scientist  is  search- 
ing for  is  the  condition  of  changes.  Something  hap- 
pens, and  he  wants  to  know  why.  He  is  on  the  outlook 
for  the  factor  which  has  led  to  the  change  in  which  he 
is  interested.  As  soon  as  I  add  sulphuric  acid  to  the 
test-tube  which  I  hold  in  my  hand,  I  begin  to  get  a 
reaction,  and  I  soon  see  a  deposit  at  the  bottom  of  the 
tube.  Cause  has,  in  short,  to  do  with  change  in  vari- 
ous parts  of  nature.  We  desire  to  know  what  disturbs 
the  previous  equilibrium  and  thus  leads  to  novelty.  A 
cause  is,  then,  a  factor  which,  so  far  as  we  can  deter- 
mine, is  the  occasion  of  the  event  which  is  selected  as 
the  effect. 

When  we  come  to  reflect  upon  the  relation  between 
a  cause  and  its  effect,  we  note  at  once  its  temporal 
character.  The  entrance  of  the  causal  factor  is  the  an- 
tecedent of  the  effect.  But  we  are  not  willing  to  con- 
sider the  entering  factor  a  cause  unless  its  absence 
involves  the  absence  of  the  effect.  It  must  be  an  indis- 
pensable antecedent.  And  it  is  not  always  easy  to 
decide  what  factor  is  indispensable.  We  must  know 
enough  about  the  field  to  make  a  good  guess  or  guesses, 
and  we  must  then  experiment  to  find  out  whether  a 
fuller  knowledge  agrees  with  the  guess. 

Post  Hoc  ergo  Propter  Hoc.  Even  the  older  logi- 
cians were  perfectly  aware  of  the  danger  of  false  gen- 
eralization.   Because  one  event  precedes  another,  we 


CAUSAL  RELATIONS  213 

must  not  jump  to  the  conclusion  that  they  are  caus- 
ally related.  If  we  take  the  antecedent  of  an  event  in 
a  purely  temporal  way,  it  includes  the  whole  range  of 
occurrences  which  can  be  dated  before  the  event  which 
we  are  interested  in.  A  causal  relation  involves  more 
than  this  temporal  antecedence;  it  implies  conviction 
that  certain  specific  events  located  in  some  definite 
part  of  space  are  most  intimately  connected  with  the 
effect.  He  who  is  on  the  outlook  for  causal  relations 
is  seeking  special  strands  of  connection.  He  wants  to 
find  constantly  repeated,  invariable,  dependable  connec- 
tions. His  ideal  is  to  analyze  nature  into  uniformities 
which  can  be  made  the  basis  of  prediction  and  control. 

Early  man  had  much  the  same  tendency  to  treat 
temporal  relations  as  causal  that  we  have  to-day,  but 
he  was  far  more  credulous  and  hasty  in  his  generaliza- 
tions. What  we  call  superstition  and  magic  consisted 
largely  of  uncritical  beliefs  of  this  character.  Chance 
association  by  contiguity  or  likeness  was  the  founda- 
tion of  accepted  laws.  The  mind  was  ruled  by  ideas 
and  made  its  selections  accordingly  with  practically  no 
thought  of  verification.  It  seemed  very  likely  that  the 
eating  of  a  lion's  heart  would  supply  courage  to  the 
warrior ;  and  had  not  B  been  unlucky  when  a  rabbit 
crossed  his  path  ?  The  selection  among  events  was  per- 
sonal and  controlled  by  chance  ideas  and  associations. 
To  the  critic  the  reply  would  have  been,  Why  not? 
And  there  was  a  dearth  of  critics.  It  took  time  and 
hard  experience  to  produce  them. 

The  tendency  to  regard  events  as  causally  related 
just  because  one  has  been  observed  to  follow  the  other 
has  been  christened  '  Post  Hoc  ergo  Premier  Hoc^ 


214  THE  ESSENTIALS  OF  LOGIC 

i.e., '  After,  therefore,  Because  of.'  "  The  history  of  the 
progress  of  hiiman  knowledge  shows,  with  increasing 
clearness,  that  better  solutions  are  given  in  proportion 
as  we  recognize  our  own  liability  to  be  misled  by  first 
appearances.  It  is  the  testing  and  verification  of 
theories,  not  the  easy  belief  that  they  need  no  testing, 
that  helps  forward  our  knowledge  of  the  ways  of 
Nature."  ^ 

Mill's  Methods.  The  human  mind  has  gradually 
hit  upon  methods  for  discovering  and  testing  causal 
relations.  These  were  first  sensed  in  the  concrete  by 
scientists  in  the  pursuit  of  particular  problems  and 
were  formulated  some  time  after  when  reflection  upon 
the  general  methods  employed  had  arisen.  The  meth- 
ods for  determining  causal  relations  were  partially 
formulated  by  Herschel  in  his  Discourse  on  the  Study 
of  Natural  Philosophy^  and  were  given  their  nearly 
final  form  by  John  Stuart  Mill.  For  this  reason,  they 
are  usually  spoken  of  as  '  Mill's  Methods.'  How  can 
causal  generalizations  be  discovered  and  verified  ?  This 
is  the  problem  around  which  they  turn. 

Mill  formulated  five  methods,  but  the  principles  in- 
volved are  essentially  two.  "The  simplest  and  most 
obvious  modes  of  singling  out  from  among  the  circum- 
stances which  precede  or  follow  a  phenomenon  (any 
event),  those  with  which  it  is  really  connected  by  an 
invariable  law,  are  two  in  number.  One  is  by  com- 
paring together  different  instances  in  which  the  phe- 
nomenon occurs.  The  other  is  by  comparing  instances 
in  which  the  phenomenon  does  occur,  with  instances  in 
other  respects  similar  in  which  it  does  not.  These  two 
*  Sidgwick,  The  Process  of  Argument,  pp.  182-33. 


CAUSAL  RELATIONS  215 

methods  may  be  respectively  denominated  the  '  Method 
of  Agreement '  and  '  Method  of  Difference.' "  These 
two  principles  would  seem  to  follow  from  the  very  nature 
of  the  causal  relation.  If  a  cause  is  the  indispensable 
antecedent  of  a  phenomenon,  can  we  not  conclude  (1) 
that  the  antecedent  in  the  absence  of  which  the  phe- 
nomenon occurs  is  not  the  cause,  and  (2)  that  the  ante- 
cedent in  whose  presence  the  phenomenon  fails  to  occur 
is  not  the  cause  ?  It  would  seem  possible,  therefore,  to 
eliminate  factors  which  are  absent  when  a  particular 
effect  occurs  and  to  test  those  which  remain  by  seeing 
whether  their  absence  involves  the  absence  of  the  effect. 
In  this  way,  resort  can  be  made  to  experimentation. 

The  Method  of  Agreement.  "  If  two  or  more 
instances  of  the  phenomenon  under  investigation  have 
only  one  circumstance  in  common,  the  circum,stance  in 
which  alone  all  the  instances  agree  is  the  cause  (or 
effect^  of  the  given  phenomenon.''^  Such  is  Mill's  state- 
ment of  the  Canon  of  Agreement.  It  is  possible  to 
represent  this  canon  schematically.  Let  X  be  the 
effect  whose  cause  we  wish  to  find,  and  let  the  accompa- 
nying circumstances  be  represented  by  abcde,  afklm,  and 
aghno  in  three  cases  of  the  appearance  of  the  effect. 
Putting  down  these  groups  in  the  above  order,  we  have : — 

ahcdeX 
afklmX 
aghnoX. 

Comparing  these  groups,  we  see  that  a  is  the  sole  factor 
which  always  accompanies  X,  and  hence  we  feel  the 
right  to  conclude  that  a  is  the  cause  of  X. 

Such  a  schematic  arrangement,  while  it  illustrates  the 


216  THE  ESSENTIALS  OF  LOGIC 

canon,  is  apt  to  be  misleading  because  of  its  simplicity 
and  artificiality.  Much  of  the  work  of  investigation 
must  be  done  before  any  such  neat  little  scheme  can  be 
constructed.  But,  after  all,  we  are  seeking  just  now  to 
get  the  principle  clearly  in  mind  and  we  can  note  the 
setting  and  difficulties  of  the  method  afterwards. 

Examples  of  Induction  by  Agreement.  One  of 
the  classic  examples  in  science  of  the  application  of  this 
method  is  the  discovery  by  Sir  David  Brewster  that  the 
material  of  mother-of-pearl  has  nothing  to  do  with  the 
brilliant  display  of  color  supposed  to  be  characteristic 
of  it.  By  accident,  he  took  an  impression  of  a  piece  of 
mother-of-pearl  in  beeswax  and  found,  much  to  his  sur- 
prise, that  the  colors  were  reproduced  upon  its  surface. 
His  interest  being  attracted,  he  carried  on  the  experi- 
ment with  other  materials  such  as  gum-arabic,  balsam, 
etc.  In  each  case,  the  colors  appeared.  The  inference 
was  obvious.  The  only  feature  these  objects  had  in  com- 
mon was  the  form  secured  by  impression  from  the 
mother-of-pearl. 

When  Sir  Isaac  Newton  was  investigating  the  prop- 
erty of  physical  objects  called  '  mass,'  he  had  to  deter- 
mine that  the  material  of  which  the  body  was  made  did 
not  affect  this  property.  In  the  same  way,  Galileo  proved 
that  bodies  fall  to  the  ground  at  a  rate  irrespective  of 
their  weight  by  the  simple  expedient  of  dropping  bodies 
of  different  weights  from  the  leaning  tower  of  Pisa. 

Let  us  suppose  that  an  epidemic  of  typhoid  fever 
has  appeared  in  a  city.  In  order  to  prevent  its  further 
spread,  the  health  authorities  will  wish  to  locate  the 
source  of  the  disease.  Past  experience  will  suggest  cer- 
tain possible  sources,  such  as  the  milk  supply,  the  water 


CAUSAL  RELATIONS  217 

supply,  the  food,  etc.  Examining  the  milk  supply,  the 
authorities  may  find  that  the  various  patients  secure 
their  milk  from  different  dairies.  This  fact  makes  the 
milk  an  improbable  source.  Turning  to  the  food  supply, 
they  may  find  that  no  one  article  of  food  is  obtained 
at  the  same  store.  The  water  supply,  on  the  other  hand, 
is  common.  This  agreement  will  suggest  to  them  very 
strongly  that  the  infection  was  spread  by  contaminated 
water.  If,  furthermore,  they  find  no  other  common 
articles  of  consumption,  they  will  undoubtedly  conclude 
that  the  water  supply  was  at  fault. 

The  Character  of  the  Method.  The  Method  of 
Agreement  is  more  one  of  observation  than  of  experi- 
mentation. As  a  rule,  a  large  number  of  instances  is 
necessary  in  order  to  make  certain  the  inclusion  of  the 
cause  among  the  factors  noted.  In  practice,  the  method 
is  preliminary  and  does  not  do  much  more  than  elimi- 
nate theoretically  possible  factors  and  narrow  down  the 
field  for  experimentation.  It  is  an  empirical  way  of 
approach  to  a  problem  and  stresses  observation.  It  does 
not  get  us  far  beneath  the  surface  of  things.  "  Thus 
varying  the  circumstances  so  as  to  bring  out  a  common 
antecedent,  though  it  does  not  end  in  exact  proof,  may 
indicate  causal  connection  though  it  does  not  prove  what 
the  nature  of  the  connection  is.  Roger  Bacon's  obser- 
vations indicated  that  the  production  of  rainbow  colors 
was  connected  with  the  passage  of  light  through  a 
transparent  globe  or  prism.  It  was  reserved  for  Newton 
to  prove  by  other  methods  that  white  light  was  composed 
of  rays,  and  that  those  rays  were  differently  refracted 
in  passing  through  the  transparent  medium."  ^ 
^  Minto,  Logic,  Inductive  and  Deductive,  p.  325. 


218  THE  ESSENTIALS  OF  LOGIC 

Difficulties  confronting  the  Method.  There  are 
two  important  difficulties  confronting  this  method. 
First  comes  the  inability  to  determine  in  any  dogmatic 
way  what  factors  are  present ;  and,  added  to  this,  the 
possibility  that  the  effect  may  be  produced  by  different 
factors  on  different  occasions.  Let  us  examine  these 
difficulties  somewhat  closely. 

It  is  so  easy  to  ignore  factors  because  they  do  not' 
seem  to  have  any  connection  with  the  effect.  Hasty 
elimination  of  factors  as  the  result  of  prejudice  can 
easily  lead  to  false  results.  Again,  analysis  is  often  too 
incomplete  to  enable  the  observer  to  recognize  the  con- 
stant factor.  A  very  good  instance  of  this  oversight  of 
the  really  important  factor  was  the  theory,  held  before 
the  part  played  by  micro-organisms  in  the  propagation 
of  disease  was  understood,  that  night  air  was  the  cause 
of  malaria.  It  was  noticed  that  people  who  caught  ma- 
laria were  generally  exposed  to  the  night  air,  but  the 
fact  that  they  were  bitten  by  mosquitoes  was  not  thought 
important  and  was  therefore  disregarded. 

The  fact  that  about  the  same  effect  can  be  produced 
by  several  causes  is  expressed  by  the  phrase,  *  plurality 
of  causes.'  Death,  for  instance,  can  be  caused  in  many 
ways,  and  so  can  headaches  and  sickness  generally. 
The  common  factor  —  when  I  take  only  a  few  cases  — 
may  not  be  the  effective  antecedent.  My  headache  may 
be  caused  one  night  by  smoking  a  cigar  and,  another 
night,  by  drinking  too  much  coffee.  We  must  conclude 
that  the  method  of  agreement  is  preliminary  and  that 
it  is  final  in  very  simple  cases  only.  The  scientist  re- 
gards it  as  a  stepping-stone  to  experimentation ;  it 
leads  to  guesses  which  can  be  tested. 


CAUSAL  RELATIONS  219 

The  Method  of  Difference.  "  If  an  instance  in 
which  the  phenomenon  under  investigation  occurs,  and 
an  instance  in  which  it  does  not  occur,  have  every  cir- 
cumstance in  common  save  one,  that  one  occurring  only 
in  thefcrrmer;  the  circumstance  in  which  alone  the  two 
instances  differ  is  the  effect  or  the  cause,  or  an  indis- 
pensable part  of  the  cause,  of  the  phenomenon^'  A  more 
''  succinct  statement  of  the  canon,  bringing  out  its  experi- 
mental character,  is  as  follows  :  "  When  the  addition  of 
an  agent  is  followed  by  the  appearance,  or  its  subtrac- 
tion by  the  disappearance,  of  a  certain  event,  other 
circumstances  remaining  the  same,  that  agent  is  the 
cause  of  the  event."  ^  It  should  be  noted  that  only  one 
factor  should  be  changed.  Great  technical  skill  is  often 
needed  to  fulfill  this  essential  condition.  The  investi- 
gator must  have  control  of  his  material. 

Examples  of  the  Method.  Suppose  we  have  been 
led  to  ask  ourselves  why  it  is  that  a  feather  does  not 
fall  to  the  ground  as  fast  as  does  a  stone.  The  idea 
may  come  to  us  that  the  presence  of  the  air  is  the 
cause.  If  we  can  remove  this  and  keep  the  other  fac- 
tors the  same,  we  will  be  able  to  test  our  conjecture. 
The  two  instances  will  be  as  follows :  — 

»        Antecedent  conditions  -Effect 

1st  instance :  stone  and  feather  dropped  in      stone  falls  first 

the  air 
2d  instance :   stone  and  feather  dropped  in      both  fall  together 
a  vacuum 

This  method  is  used  primarily  in  physics  and  chem- 
istry, for  the  material  of  these  sciences  lends  itself  to 
a  literal  analysis  and  synthesis  under  experimental  con- 
1  Mellone,  An  Introductory  Text-Bo<Jc  of  Logic,  p.  274. 


220  THE  ESSENTIALS  OF  LOGIC 

ditions.  It  is  less  easy  to  apply  it  to  organisms  and  to 
social  conditions. 

Warnings.  When  the  method  can  be  applied  under 
experimental  conditions  so  that  only  one  factor  varies, 
the  only  danger  lies  in  the  interpretation  of  the  result. 
The  factor  may  not  be  the  only  cause  which  is  able  to 
produce  the  effect.  A  plant  may  die  when  water  is 
withheld,  but  it  will  also  die  when  heat  is  removed.  A 
positive  effect  often  demands  the  cooperative  presence 
of  many  conditions,  and  then  the  removal  of  any  one 
of  these  will  prevent  the  occurrence  of  the  effect.  An- 
other difficulty  lies  in  the  possible  presence  of  counter- 
acting causes.  A  man  who  is  very  healthy  may  be  able 
to  resist  infection,  and  so  may  a  man  who  has  had  the 
disease  and  is  now  immune.  So  long  as  there  is  incom- 
plete analysis  of  the  situation,  interpretation  of  the 
result  of  an  experiment  has  its  dangers.  Only  as  fur- 
ther knowledge  is  gained,  does  the  only  possible  inter- 
pretation begin  to  stand  out. 

When  experimental  conditions  cannot  be  obtained, 
there  is  great  danger  that  the  two  instances  may 
differ  in  more  than  one  point.  "  As  an  exemplifi- 
cation of  this,  we  may  cite  an  inference  that  was  sup- 
posed to  be  warranted  by  the  experience  of  one  of  our 
larger  cities,  which  had  voted  to  increase  materially 
the  price  of  liquor  licenses.  The  police  records,  for  the 
period  immediately  subsequent  to  the  time  when  the 
new  law  went  into  effect,  showed  a  distinct  decrease  in 
the  amount  of  crime.  By  the  method  of  difference  we 
should  naturally  attribute  this  fact  to  the  high  license. 
But  it  was  found  that  after  the  election  the  officials 
who  issued  the  licenses  had  been  much  more  careful 


CAUSAL  RELATIONS  221 

than  before  to  issue  licenses  only  to  applicants  of  good 
moral  character.  This  fact  alone  might  account  for  the 
decrease  in  crime,  leaving  the  higher  license  without 
effect  upon  the  result."  ^ 

The  Method  of  Concomitant  Variations. 
"  Whatever  phenomenon  varies  in  any  manner^  when- 
ever another  phenomenon  varies  in  some  particular 
manner^  is  either  a  cause  or  an  effect  of  that  phenom- 
enon^ or  is  connected  with  it  through  some  fact  of 
causation.'^  The  development  of  quantitative  methods 
in  modern  science  has  made  it  possible  to  measure  the 
variations  of  the  important  antecedents  of  an  effect 
and  to  note  corresponding  variations  in  the  effect 
itself.  This  mode  of  procedure  is  especially  valuable 
when  the  conjectured  cause  cannot  be  removed  com- 
pletely but  only  decreased  and  increased.  The  method 
can  be  used  either  as  a  substitute  for  the  Method  of 
Difference  or  as  a  reinforcement  of  it  when  the  interest 
of  the  experimenter  travels  to  the  study  of  the  quanti- 
tative aspects  of  the  causal  relation. 

Examples  of  the  Method.  The  history  of  science 
is  replete  with  instances  of  the  application  of  the 
Method  of  Concomitant  Variation.  By  the  experiment 
of  Count  Rumford,  heat  was  shown  to  be  the  effect  of 
motion.  "  In  this  famous  experiment,  which  disproved 
the  material  theory  of  heat,  a  blunt  steel  borer  3^ 
inches  wide  was  turned  by  horse  power  32  times  a 
minute  inside  a  brass  cylinder  weighing  113  pounds. 
In  two  and  a  half  hours  the  water  surrounding  the 
cylinder  and  weighing  18|  pounds  was  heated  from 
60°  F.  to  the  boiling  point.  Only  4145  grains  of 
^  Bode,  An  Outline  of  Logic,  p.  139. 


222  THE  ESSENTIALS  OF  LOGIC 

the  metal  were  abraded.  Rumford  correctly  concluded 
that  this  large  amount  of  heat,  which  appeared  to  be 
inexhaustible,  could  not  have  been  derived  from  the 
abraded  metal,  which  at  the  same  time  had  not  lost 
any  of  its  capacity  for  heat."  ^  The  First  Law  of 
Motion,  Boyle's  Law,  the  theory  of  the  thermometer, 
the  connection  of  air  with  the  propagation  of  sound 
are  all  dependent,  in  whole  or  in  part,  upon  the  use  of 
this  method. 

Warning.  This  method  stresses  the  ratio  between 
the  change  in  the  causal  factor  and  the  change  in  the 
effect.  It  has  been  found,  however,  that  there  is  such 
a  thing  as  discontinuous  variation.  Metals  do  not 
continue  to  expand  at  the  same  rate  as  the  temperature 
increases,  nor  do  they  contract  at  the  same  rate  as  the 
temperature  is  lowered.  Another  point  should  be 
noted.  It  often  happens  that  both  of  the  quantities 
measured  are  co-effects  of  a  third  factor.  Hence,  where 
possible,  the  Method  of  Concomitant  Variations  should 
be  supplemented  by  the  Method  of  Difference. 

The  Joint  Method  of  Agreement  and  Differ- 
ence. "  ^  two  or  more  instances  in  which  the  phe- 
nomenon occurs  have  only  one  circumstance  in  com- 
mon, while  two  or  more  instances  in  which  it  does  not 
occur  have  nothing  in  common  save  the  absence  of  that 
circumstance,  the  circumstance  in  which  alone  the  two 
sets  of  instances  differ  is  the  effect,  or  the  cause,  or  an 
indispensable  part  of  the  cause,  of  the  'phenomenon^ 
The  Joint  Method  is  a  combination  of  the  Method  of 
Agreement  and  the  Method  of  Difference,  and  is  espe- 
cially applicable  when  experimental  conditions  are  not 
^  Carhart,  University  Physics,  pt.  u,  p.  4. 


CAUSAL  RELATIONS  223 

obtainable.  It  is  a  method  of  group  comparisons.  The 
investigator  collects  cases  in  which  the  desired  effect 
is  present  and  compares  the  instances  to  see  in  what 
they  agree ;  he  then  collects  other  cases  in  which  the 
effect  is  absent  and  compares  these  instances  to  see  in 
what  they  agree.  Finally,  he  examines  the  two  groups 
to  see  wherein  they  differ.  In  this  way,  he  approaches 
as  nearly  to  the  Method  of  Difference  as  can  be  done 
without  experimentation.  Without  some  control  of  the 
factors,  the  conclusion  can  be  regarded  only  as  tenta- 
tive. 

iEzamples.  "  The  following  instance  illustrates  the 
use  of  the  Joint  Method  of  Agreement  and  Difference : 
A  large  number  of  cases  of  typhoid  fever  occurred  at 
about  the  same  time  in  a  college  community.  It  hap- 
pened that  all  those  who  developed  the  disease  ate  at  a 
certain  few  fraternity  and  boarding-house  tables.  The 
water  supply  was  first  investigated.  It  was  found  that 
all  these  places  used  water  from  the  same  source.  But 
it  was  also  true  that  the  other  houses  were  supplied 
from  the  same  source,  so  this  possible  cause  was  elimi- 
nated. The  fresh  vegetables  were  supplied  from  vari- 
ous sources ;  some  of  the  places  in  which  the  disease 
was  developed  used  one  source,  others  a  different  one ; 
moreover,  the  places  in  which  the  disease  was  not  de- 
veloped were  supplied  from  the  same  variety  of  sources. 
The  other  food  supplies  came  from  various  places  and 
the  Method  of  Agreement  could  not  be  applied  so  far 
as  they  were  concerned,  with  one  exception  ;  it  appeared 
that  the  milk  supply  was  the  same  for  all  the  places  in 
which  the  fever  was  developed,  whereas  none  of  the 
places  which  escaped  used  milk  from  that  source.  The 


9M  THE  ESSENTIALS  OF  LOGIC 

inference  was  that  the  milk  contained  the  cause  of  the 
disease.  Further,  it  was  found  that  when  milk  from 
this  source  was  no  longer  used,  no  new  cases  of  the  dis- 
ease appeared."  ^  Another  good  e;cample  is  to  be  found 
in  the  work  of  Darwin  upon  the  cross-fertilization  of 
flowers.  In  this  investigation,  Darwin  placed  a  net 
about  one  hundred  flower  heads  to  protect  them  from 
bees.  At  the  same  time  he  exposed  another  hundred 
flowers  to  the  bees.  Here  we  have  the  two  groups  be- 
tween which  comparison  is  to  be  made.  He  obtained 
the  following  results  :  The  protected  flowers  failed  to 
yield  a  single  seed,  while  the  others  produced  68  grains' 
weight  of  seed,  which  he  estimated  as  numbering  2720 
seeds. 

These  examples  show  that  the  Joint  Method  is  really 
the  complete  application  of  the  two  principles  of  Agree- 
ment and  Difference,  and  that  any  exhaustive  investi- 
gation is  bound  to  take  this  form.  Another  point  stands 
out  clearly.  In  any  actual  study  the  mind  is  always 
making  conjectures  and  testing  them  by  these  methods. 
The  scientist  is  not  a  merely  passive  tabulator.  He 
knows  that  the  cause  must  be  present  when  the  effect  is, 
and  that  it  must  be  absent  when  the  effect  is  absent. 
Hence,  he  is  on  the  constant  lookout  for  factors  which 
may  fulfill  these  conditions. 

The  Method  of  Residues.  "  Suhduct  from  any 
phenomenon  such  part  as  is  known  by  previous  induc- 
tions to  be  the  effect  of  certain  antecedents,  and  the  res- 
idue of  the  phenomenon  is  the  effect  of  the  remaining 
antecedents."  This  method  can  be  employed  only  when 
there  is  nearly  complete  information  in  regard  to  the 
1  Jones,  Logic,  Inductive  and  Deductive,  pp.  98-09. 


CAUSAL  RELATIONS  225 

field  under  investigation.  By  means  of  this  knowledge, 
we  are  able  to  eliminate  causal  couples  until  we  are  left 
with  the  few  factors  remaining  for  which  causal  rela- 
tions have  not  been  determined.  In  this  way,  past 
knowledge  enables  the  investigator  to  narrow  the  field. 
After  this  is  accomplished,  he  can  observe  more  closely 
and  often  experiment.  Like  the  Method  of  Agreement, 
the  Method  of  Residues  is  usually  a  preliminary  pro- 
cess which  needs  supplementation. 

Examples.  The  Method  of  Residues  comes  out 
most  clearly  where  quantitative  methods  are  being  em- 
ployed. For  astronomy,  the  classic  example  is  the  dis- 
covery of  the  planet  Neptune.  Certain  perturbations  in 
the  movement  of  Uranus  could  not  be  accounted  for 
by  known  gravitational  forces.  The  natural  inference 
was  that  some  unknown  planet  was  at  work  producing 
this  added  increment,  the  residual  effect.  Adams  in 
England  and  Leverrier  in  France  made  this  hypothesis 
independently  of  each  other  and  calculated  the  prob- 
able place  of  the  new  planet.  Following  the  directions 
of  the  latter.  Professor  Galle,  of  Berlin,  found  the  new 
planet  in  almost  exactly  the  place  indicated.  Another 
instance  of  discovery  due  to  residual  effects  is  that  of 
the  rarer  elements  in  the  atmosphere  such  as  argon  and 
helium.  "In  chemical  analysis  this  method  is  con- 
stantly employed  to  determine  the  proportional  weight 
of  substances  which  combine  together.  Thus  the  com- 
position of  water  is  ascertained  by  taking  a  known 
weight  of  oxide  of  copper,  passing  hydrogen  over  it  in 
a  heated  tube,  and  condensing  the  water  produced  in 
a  tube  containing  sulphuric  acid.  If  we  subtract  the 
original  weight  of  the  condensing  tube  from  its  final 


226  THE  ESSENTIALS  OF  LOGIC 

weight  we  learn  how  much  water  is  produced ;  the 
quantity  of  oxygen  in  it  is  found  by  subtracting  the 
final  weight  of  the  oxide  of  copper  from  its  original 
weight.  If  we  then  subtract  the  weight  of  the  oxygen 
from  that  of  the  water  we  learn  the  weight  of  the  hy- 
drogen, which  we  have  combined  with  the  oxygen."  ^ 

This  method  is  primarily  one  of  quantitative  analy- 
sis. It  concerns  itself  with  residual  phenomena,  with 
exceptions.  Speaking  of  his  father,  Francis  Darwin 
says :  "  There  was  one  quality  of  mind  which  seemed  to 
be  of  special  and  extreme  advantage  in  leading  him  to 
make  discoveries.  It  was  the  power  of  never  letting 
exceptions  pass  unnoticed."  Such  a  habit  of  mind  is 
assuredly  worth  cultivation. 

Remarks  on  Mill's  Methods.  There  is  pretty 
general  agreement  now  among  logicians  that  Mill's 
Methods  can  be  employed  only  within  a  larger  induc- 
tive setting.  They  are  not  rules  which  can  be  applied 
mechanically  to  new  and  complex  fields.  The  mind 
must  be  active  in  conjecture,  interpretation  and  analy- 
sis. In  the  first  part  of  his  Logic,  Mill  is  far  more  Bacon- 
ian than  he  is  in  the  latter  part.  The  following  quota- 
tion gives  all  the  correction  that  is  needed  and  reveals 
how  the  Methods  are  taken  up  into  the  concrete  process 
of  investigation  :  "  The  process  of  tracing  regularity  in 
any  complicated,  and  at  first  sight  confused  set  of  ap- 
pearances, is  necessarily  tentative  :  we  begin  by  making 
any  supposition,  even  a  false  one,  to  see  what  conse- 
quences will  follow  from  it;  and  by  observing  how 
these  differ  from  the  real  phenomena,  we  learn  what 
corrections  to  make  in  our  assumption."  Increasing 
^  Jevons,  Lessons  in  Logic,  p.  254. 


CAUSAL  RELATIONS  227 

analysis,  working  hypotheses,  gradual  elimination  of 
irrelevant  factors,  and  final  decision  as  to  the  essential 
connections  are  the  steps  in  induction. 

REFERENCES 

Creighton,  An  Introductory  Logic,  chaps,  xvi  and  xvn. 

Gibson,  The  Problems  of  Logic,  chap.  xin. 

Jones,  Logic,  Inductive  and  Deductive,  chap.  VI. 

Mill,  Logic,  bk.  ui,  chaps,  vin  and  ix. 

Minto,  Logic,  Inductive  and  Deductive,  bk.  n,  chaps,  m,  rv,  and  v. 


CHAPTER  XX 

STATISTICS 

In  many  fields  of  investigation  it  is  impossible  to 
apply  the  traditional  methods.  The  problem  is  of  such 
a  character  and  covers  such  a  wide  territory  that  indi- 
vidual observation  cannot  furnish  the  factual  material. 
Furthermore,  experimental  methods  cannot  be  applied. 
What  is  needed  is  a  very  broad  survey  of  the  facts  and 
a  clear  tabulation  of  the  results  obtained.  Out  of  this 
necessity  has  arisen  statistical  science.  "It  would  be  a 
man  of  exceptional  mnemonic  power  who  could,  after 
listening  to  the  reading  of  two  lists  of  one  hundred 
items  each  stating  the  names  and  wealth  of  the  respec- 
tive inhabitants  of  two  villages,  give  any  intelligent 
opinion  as  to  the  comparative  riches  of  the  two  communi- 
ties. If  this  is  true  for  such  small  groups  as  this,  it  evi- 
dently would  be  utterly  impossible  to  make  comparisons 
of  the  wealth  of  great  nations  without  some  manner  of 
reducing  the  mass  of  separate  facts  to  a  simple  whole. 
The  same  would,  of  course,  be  true  in  the  case  of  any 
other  phenomena  involving  large  numbers.  What  could 
one  understand  of  the  amount  of  lumber  contained  in  a 
forest  from  a  description  of  the  separate  trees  ?  How 
could  one  compare  the  climates  of  difi'erent  localities  by 
a  study  of  their  daily  weather  records  ?  It  is  for  the 
purpose  of  simplifying  these  unwieldy  masses  of  facts 
that  statistical  science  is  useful.  It  reduces  them  to 
numerical  totals  or  averages  which  may  be  abstractly 


STATISTICS  229 

handled  like  any  other  mere  numbers.  It  draws  pictures 
and  diagrams  to  illustrate  general  tendencies  and,  thus, 
in  many  ways  adapts  these  groups  of  ideas  to  the  capac- 
ity of  our  intellects."  ^ 

If  the  student  will  recall  the  discussion  of  "  Classi- 
fication," he  will  remember  that  it  was  regarded  as  a 
process  which  enables  us  to  handle  the  complex  world 
of  individual  things  in  which  we  live.  Could  we  not 
treat  things  as  kinds  and  know  what  to  expect  from 
them,  we  should  be  unable  to  adapt  ourselves  to  our 
environment  by  using  our  past  experience.  Now,  statis- 
tics is  a  way  of  dealing  with  particulars  which  can  be 
counted  and  which  are  so  numerous  that  we  need  to 
achieve  some  bird's-eye  view  of  them  before  we  can 
begin  to  interpret  them.  It  is  a  way  of  collecting  and 
organizing  data  which  are  important  in  masses  rather 
than  individually.  "  The  proper  function  of  statistics," 
writes  Bowley,  "  is  to  enlarge  individual  experience." 
Originally  the  workers  in  statistics  concerned  them- 
selves almost  entirely  with  facts  respecting  the  condition 
of  the  people  in  a  state,  but  now  data  in  biology  and 
astronomy  are  also  investigated  by  statistical  methods. 

We  have  frequently  pointed  out  that  science  always 
involves  analysis.  Mental  work  must  be  done  upon  the 
facts  before  they  yield  a  meaning  and  can  be  applied 
to  the  solution  of  a  problem.  This  element  stands  out 
very  clearly  in  the  following  definition  of  statistics : 
"  The  science  of  statistics  is  the  method  of  judging  col- 
lective natural  or  social  phenomena  from  the  results 
obtained  by  the  analysis  of  an  enumeration  or  collec- 
tion of  estimates."  2 

1  King,  Elements  of  Statistical  Method,  p.  24.  «  Ibid.,  p.  23. 


2S0  THE  ESSENTIALS  OF  LOGIC 

The  stages  in  a  statistical  investigation  are  roughly 
as  follows :  (1)  The  setting  of  the  problem ;  (2)  the 
collection  of  the  material ;  (3)  its  tabulation  ;  (4)  the 
summary ;  (5)  a  critical  examination  of  the  results. 
Let  us  look  at  these  stages  somewhat  closely. 

"  Special  importance,  it  seems,  must  be  attached  to 
the  question  of  what  are  the  objects  of  any  particular 
statistical  record.  It  is  not  enough  to  observe  the  facts 
at  random.  Most  of  the  records  of  statistics,  although 
not  all  of  them,  are  deliberately  arranged  to  be  kept  by 
a  community  for  the  purpose  of  the  information  of  the 
whole  community.  .  .  .  The  object,  then,  of  any  par- 
ticular statistical  record  is  the  first  thing  about  it  to  be 
studied,  and  both  the  Government  in  making  the  rec- 
ords and  the  students  who  come  to  use  them  afterwards 
should  have  the  most  distinct  ideas  upon  this  point."  ^ 
This  point  is  stressed  by  all  statisticians.  "  The  first 
thing  upon  which  the  statistical  investigator,  when  be- 
ginning his  work,  must  decide  is  the  exact  nature  of 
the  problem  which  he  desires  to  solve.  Even  a  slight 
change  in  its  scope  or  form  may  require  an  entirely  or 
partially  different  method  of  procedure.  If,  for  illustra- 
tion, a  person  wishes  to  begin  a  study  of  comparative 
wages  in  order  to  demonstrate  some  general  theory  or 
proposition,  he  must  first  decide  as  to  whether  the  re- 
quirements of  his  problem  demand  a  knowledge  of 
money  wages  or  real  wages.  Next,  he  must  be  sure  as  to 
whether  he  needs  to  know  the  wages  paid  for  a  definite 
amount  of  effort,  for  making  a  certain  product,  or  for 
working  a  certain  length  of  time,  or  whether  the  in- 
quiry relates  to  the  income  of  the  working  man  him- 
^  Sir  Robert  GifEen,  Statistics,  pp.  4-5. 


STATISTICS  231 

self  per  year  or  to  the  total  income  of  the  man  and 
his  family  for  the  same  period.  Each  of  these  problems 
is  a  distinct  one  and  would  require  entirely  different 
modes  of  determination."  ^ 

Definition  of  the  problem  also  involves  definition  of 
the  unit.  What  shall  we  mean  by  '  unemployment '  ?  by 
*  person '  ?  by  '  a  farm  '  ?  by  '  sickness  '  ?  Just  as  classi- 
fication and  its  principles  are  important  for  statistical 
investigation,  so  is  definition.  Thus  a  recent  work  on 
Unemployment  gives  a  chapter  to  the  "  Meaning  and 
Measurement  of  Unemployment "  and  devotes  much  of 
its  space  to  the  working-out  of  a  definition.  "  Are  we, 
for  example,  to  include  among  the  unemployed  those 
who  are  idle  because  they  do  not  want  to  work?  Are 
we  to  include  sick  persons,  or  workmen  out  on  strike, 
or  the  various  classes  of  individual  who  are,  for  one 
reason  or  another,  'unemployable'?"  Just  as  an  idea 
must  not  be  allowed  to  change  its  meaning  in  the  course 
of  an  argument,  so  the  unit  must  not  be  altered  in  the 
course  of  an  investigation.  The  prerequisites  of  clear 
thinking  are  essentially  the  same  for  argument  of  a 
deductive  character  and  for  investigation. 

Before  the  collection  of  the  material  is  begun,  the 
problem  must  be  studied  in  all  its  details.  "  Problems, 
factors,  units,  questions,  schedules,  enumerators,  tabu- 
lation, methods  of  work,  time,  expense,  etc.,  are  among 
the  items  that  must  be  carefully  gone  over  in  minute 
detail."  The  methods  of  collection  must  be  determined 
by  experience  with  due  regard  to  the  characteristics  of 
the  particular  problem.  The  field  must  be  defined  and 
must  be  as  wide  as  possible.  If  questions  are  used,  these 
^  King,  Elements  of  Statistical  Method,  p.  39. 


282  THE  ESSENTIALS  OF  LOGIC 

must  be  comparatively  few  in  number,  must  be  simple 
enough  to  be  readily  understood,  and  must  not  arouse 
prejudices.  As  in  all  the  other  divisions  of  science,  per- 
sonal judgment  cannot  be  eliminated.  Investigation  is 
not  a  mechanical  process. 

"  With  the  collection  of  statistical  data,  only  the  first 
step  has  been  taken.  The  statistics  in  that  condition  are 
only  raw  material  showing  nothing.  They  are  not  an 
instrument  of  investigation  any  more  than  a  kiln  of 
bricks  is  a  monument  of  architecture.  They  need  to  be 
arranged,  classified,  tabulated,  and  brought  into  con- 
nection with  other  statistics  by  the  statistician.  Then 
only  do  they  become  an  instrument  of  investigation, 
just  as  a  tool  is  nothing  more  than  a  mass  of  wood  or 
metal,  except  in  the  hands  of  a  skilled  workman."  ^  The 
figures  must  be  grouped  in  tables  under  appropriate 
headings  in  such  a  way  as  to  bring  out  the  desired  per- 
centages and  correlations.  "  The  power  to  analyze  a 
table,  interpret  the  results  correctly,  and  state  the  con- 
clusions lucidly  and  succinctly  is  one  of  the  character- 
istics indispensable  in  a  good  statistician." 

The  Law  of  Statistical  Regularity.  It  has  been 
discovered  that  a  moderately  large  number  of  items 
taken  at  random  from  a  very  large  group^  are  almost 
sure,  on  the  average,  to  have  the  characteristics  of  the 
larger  group.  "  Thus,  if  two  persons,  blindfolded,  were 
to  pick  here  and  there  three  hundred  walnuts  each  from 
a  bin  containing  a  million  nuts,  the  average  weight  of 
the  nuts  picked  out  by  each  person  would  be  almost 
identical  even  though  the  nuts  varied  considerably  in 
size."  Corresponding  to  this  law  is  its  corollary,  the 
^  Mayo-Smith,  Statistics  and  Sociology,  p.  18. 


STATISTICS  233 

law  of  inertia  of  large  numbers.  Logicians  have  been 
accustomed  to  speak  of  this  law  as  the  constancy  of 
averages.  "  If  we  take  a  succession  of  periods,  and  di- 
vide the  total  number  of  any  kind  of  event  by  the  num- 
ber of  periods,  we  get  what  is  called  the  average  for 
that  period:  and  it  observed  that  such  averages  are 
maintained  from  period  to  period.  Over  a  series  of 
years  there  is  a  fixed  proportion  between  good  harvests 
and  bad,  between  wet  days  and  dry :  every  year  nearly 
the  same  number  of  suicides  takes  place,  the  same  num- 
ber of  crimes,  of  accidents  to  life  and  limb,  even  of  sui- 
cides, crimes,  or  injuries  by  particular  means:  every 
year  in  a  town  nearly  the  same  number  of  children 
stray  from  their  parents  and  are  restored  by  the  police : 
every  year  nearly  the  same  number  of  persons  post 
letters  without  putting  an  address  on  them."  ^ 

Dangers  in  the  Use  of  Statistics.  Great  care 
must  be  taken  in  the  use  of  statistics.  It  has  been  said 
that  "  you  can  prove  anything  by  statistics."  And  this 
skepticism  reflects  the  constant  misuse  of  figures.  Every 
stage  in  the  development  of  tables  is  liable  to  its  pecul- 
iar errors  which  resemble  those  which  face  all  inves- 
tigation. Prejudice,  inaccuracy,  faulty  observation, 
mistakes  in  copying,  wrong  interpretation,  all  exist  as 
possible  sources  of  falsehood.  Another  cause  of  error  is 
the  lack  of  recognition  given  to  the  difference  between 
quantity  and  quality.  "  In  sociological  science  the  im- 
portance of  differences  of  quality  is  enormous,  and  the 
effect  of  these  differences  on  the  conclusions  to  be 
drawn  from  figures  is  sometimes  neglected,  or  insuffi- 
ciently recognized,  even  by  men  of  unquestionable 
^  MiDto,  Logic,  Inductive  and  Deductive,  p.  351. 


284  THE  ESSENTIALS  OF  LOGIC 

ability  and  good  faith.  The  majority  of  politicians,  so- 
cial '  reformers '  and  amateur  handlers  of  statistics  gen- 
erally are  in  the  habit  of  drawing  the  conclusions  that 
seem  good  to  them  from  such  figures  as  they  may  ob- 
tain, merely  by  treating  as  homogeneous  quantities 
which  are  heterogeneous,  and  as  comparable  quantities 
which  are  not  comparable.  Even  to  the  conscientious 
and  intelligent  inquirer  the  difficulty  of  avoiding  mis- 
takes in  using  statistics  prepared  by  other  persons  is 
very  great.  There  are  usually  '  pitfalls '  even  in  the 
simplest  statistical  statement,  the  position  and  nature 
of  which  are  known  only  to  the  persons  who  have  actu- 
ally handled  what  may  be  called  the  '  raw  material '  of 
the  statistics  in  question ;  and  in  regard  to  complex 
statistical  statements  the  '  outsider '  cannot  be  too  care- 
ful to  ascertain  from  those  who  compiled  them  as  far 
as  possible  what  are  the  points  requiring  elucidation.  "^ 
So  frequent  a  use  is  made  of  statistics  now  that  the 
logician  feels  it  a  part  of  his  duty  to  stress  these 
warnings.  The  following  example  may  serve  to  indicate 
how  easily  fallacy  may  creep  in :  "  An  example  of  such 
a  fallacy,  due  to  the  use  of  erroneous  factors,  was  fur- 
nished by  a  newspaper  in  a  discussion  of  the  American 
navy  during  the  Spanish-American  War.  It  was  stated 
that  the  death-rate  in  the  navy  during  the  war  period 
was  only  nine  per  thousand,  while  in  the  city  of  New 
York  for  the  same  period  the  death-rate  was  sixteen 
per  thousand.  The  conclusion  was  drawn  that  it  was 
safer  to  be  a  sailor  in  our  navy  in  war-time  than  to  live 
in  New  York  City.  A  little  reflection,  however,  will 
convince  one  that  such  a  conclusion  is  not  warranted 
^  Encyclcpcedia  Britannica,  art. "  Statistics." 


\ 


STATISTICS  235 

by  the  figures  given.  In  obtaining  this  ratio,  the  total 
number  of  deaths  was  taken  as  the  numerator  in  each 
case  and  the  denominators  were  respectively  the  total 
number  of  persons  living  in  New  York  City  and  the 
total  number  of  sailors  in  the  navy.  But,  as  a  matter 
of  fact,  these  numbers  were  wholly  incomparable.  It  is 
a  well-known  fact  that  the  death-rate  is  very  high 
among  young  children  and  among  old  people.  But  the 
personnel  of  the  navy  is  composed  almost  wholly  of 
young  men  in  the  prime  of  strength  and  vigor.  Not 
only  this,  but  each  must  pass  a  strict  examination  to 
show  that  he  is  healthy  and  robust.  Thus,  the  weak 
and  diseased  are  eliminated.  Evidently,  the  facts  would 
require  that  the  death-rate  in  the  navy  be  compared 
with  the  death-rate  of  a  similar  picked  body  of  men  in 
New  York  City  before  any  legitimate  conclusions  could 
be  drawn  regarding  the  comparative  chances  of  death 
in  the  two  places."  ^ 

The  Value  of  Statistics.  There  are  three  main 
ends  subserved  by  statistics :  Its  employment  contrib- 
utes to  a  descriptive  survey  of  a  field  which  cannot  be 
otherwise  grasped.  Figures  are  then  merely  a  method 
of  expressing  facts,  as  the  amount  of  wheat  produced, 
the  quantity  of  exports,  the  amount  of  the  national 
wealth.  Such  information  is  often  of  the  greatest  sig- 
nificance. We  may  wish  to  compare  one  country  with 
another,  or  the  same  country  at  different  times.  Very 
frequently  the  data  obtained  can  be  used  to  test  a  theory 
which  has  been  worked  out  more  or  less  deductively. 
Wherever  there  is  induction,  there  must  be  appeal  to 
relevant  fact ;  and  in  many  fields,  statistics  is  the  only 
*  King,  Elements  of  Statistics,  p.  40. 


236  THE  ESSENTIALS  OF  LOGIC 

means  of  securing  such  facts.  In  the  second  place,  the 
discovery  of  averages  which  are  fairly  constant  enables 
man  to  predict  the  general  run  of  cases  in  the  future. 
As  we  shall  see  in  the  next  chapter,  the  theory  and 
practice  of  life  insurance  are  founded  upon  the  exist- 
ence of  such  averages  which  are  being  continually  de- 
veloped and  rendered  more  accurate.  In  the  third 
place,  tables  of  statistics  often  reveal  correlations  which 
would  not  otherwise  have  been  discovered  because  of 
the  complexity  of  the  material  and  our  inability  to  ana- 
lyze it  into  distinct  strands  of  causal  uniformities. 
When  data  are  properly  arranged,  the  field  is  condensed 
and  simplified  and  it  is  possible  to  note  relations  which 
would  have  remained  hidden.  The  use  of  graphs  is 
often  an  aid  because  they  make  a  direct  appeal  to  the 
eye.  An  example  of  a  correlation  which  suggests  the 
presence  of  causal  relations  is  the  fluctuation  of  the  num- 
ber of  births  in  a  country  correspondent  with  the  food 
prices  of  the  previous  year.  Let  us  consider  this  third 
function  of  statistics  a  little  more  fuUy. 

The  principle  underlying  the  deduction  of  causal  re- 
lations from  correlations  is  the  assumption  that  if  the 
events  are  unconnected,  their  frequencies  should  not 
fluctuate  together  nor  coincide  beyond  a  certain  amount. 
Bain  formulated  the  following  rule :  "  Consider  the 
positive  frequency  of  the  phenomena  themselves,  and 
how  great  frequency  of  coincidence  must  foUow  from 
that,  supposing  there  is  neither  connection  nor  repug- 
nance. If  there  be  greater  frequency,  there  is  connec- 
tion ;  if  less,  repugnance."  Repugnance  is  usually  spoken 
of  in  statistics  as  negative  correlation.  An  example 
would  be  the  relation  between  vaccination  and  small- 


STATISTICS  237 

pox.  In  delicate  cases,  it  is  very  difficult  to  estimate 
the  degree  of  coincidence  between  non-causal  events. 
How  often,  for  instance,  must  dreams  and  their  apparent 
fulfillment  coincide  to  pass  beyond  mere  coincidence  ? 

Variation  in  averages  is  a  fruitful  source  for  the  dis- 
covery of  causal  relations.  If  we  assume  that  the  con- 
stancy of  the  averages  is  due  to  the  maintenance  of  the 
relative  proportions  of  the  same  factors  in  the  field 
under  investigation,  then  any  change  in  the  average 
must  be  due  to  an  alteration  in  this  proportion  or  to 
the  entrance  of  a  new  factor.  A  study  of  the  geo- 
graphical distribution  of  suicide  is  a  good  instance  of 
the  suggestive  character  of  comparative  statistics.  We 
immediately  ask  ourselves  why  one  country  leads,  what 
can  be  the  peculiar  conditions  which  cause  more  people 
to  commit  suicide  there.  It  will  be  noted  that  such 
comparison  involves  a  near  approach  to  the  method  of 
differences.  But  experiment  is  impossible.  When  an 
average  begins  to  change,  the  investigator  seeks  the  pres- 
ence of  some  new  cause  or  the  increase  of  some  cause 
already  operative.  "  The  number  of  homicides  in  the 
United  States  in  1894  far  exceeded  the  annual  num- 
ber observed  for  the  years  preceding.  This  discrepancy 
is  easily  accounted  for  by  the  fact  that  the  natural 
number  was  swollen  by  the  deaths  caused  by  the  strik- 
ers and  rioters  in  the  month  of  July  of  that  year.  So 
also  a  marked  departure  from  the  annual  death-rate  of 
such  a  city  as  New  York  is  at  once  an  urgent  sugges- 
tion to  the  Board  of  Health  to  start  investigations  that 
will  unearth  the  hidden  cause  that  one  is  constrained 
to  believe  must  be  present.  Such  causes  as  defective 
drains,  prevalence   of  epidemics,  etc.,  are  again  and 


288  THE  ESSENTIALS  OF  LOGIC 

again  found  to  accompany  an  increase  of  the  average 
death-rate."  ^  The  principle  involved  is  essentially  that 
of  concomitant  variation. 

REFERENCES 

King,  Elements  of  Statistical  Method,  chaps,  I,  ll,  and  in. 

Bowley,  Elements  of  Statistics,  passim. 

Giffen,  Statistics,  chap.  i. 

Creighton,  An  Introductory  Logic,  chap.  xv. 

Elderton,  Primer  of  Statistics. 

Hibben,  Logic,  Deductive  and  Inductive,  chap.  XV. 

Mayo-Smith,  Statistics  and  Sociology,  chaps,  i,  u,  and  m. 

^  Hibben,  Logic,  Deductive  and  Inductive,  p.  344. 


CHAPTER  XXI 

PROBABILITY 

Abstract  Laws  versus  Concrete  Events.  While 
the  physical  sciences  are  chiefly  interested  in  the  dis- 
covery of  universally  valid  causal  laws  and  in  the 
construction  of  illuminating  general  principles  and 
theories,  problems  of  another  sort  come  to  the  front  in 
practical  life,  the  applied  sciences,  and  those  fields  of 
research  in  which  experimental  control  is  impossible. 
Where  experiment  is  possible,  factors  can  be  eliminated 
as  irrelevant  or  confusing,  and  the  remaining  elements 
can  then  be  analyzed  into  couples  uniformly  connected. 
But  where  such  experimental  control  and  simplification 
is  out  of  the  question,  causes  counteract  one  another  in 
the  most  complex  ways  or  else  combine  to  produce 
effects  which  are  not  deducible  from  any  one  of  them. 
In  other  words,  such  causal  uniformities  as  we  discover 
by  experiment  are  blurred  when  they  enter  this  whirli- 
gig of  a  world,  and  it  is  with  the  greatest  uncertainty 
that  we  predict  the  course  of  events. 

In  science,  the  investigator  usually  passes  from  effect 
to  cause;  in  everyday  life,  the  problem  is  to  pass  from 
the  play  of  events  to  the  probable  result.  What  it  is 
now  desired  to  ascertain  is  what  will  probably  happen 
in  the  tangled  skein  of  events  which  cannot  be  com- 
pletely analyzed  beforehand.  Will  the  country  be 
prosperous  a  year  from  now  or  plunged  in  a  panic? 
Will  this  bank  be  solvent  or  will  it  fail?   Will  the 


240  THE  ESSENTIALS  OF  LOGIC 

crops  be  good  this  year?  Such  questions  make  us 
realize  the  complexity  of  things  and  our  inability  to 
deduce  events  from  the  few  uniformities  we  have  as 
yet  discovered.  Most  laws  have  their  exceptions  be- 
cause the  essential  factors  are  masked  by  the  interplay 
of  their  fellows. 

Where  Certainty  is  possible.  Certainty  as  to  the 
future  is  possible  only  when  all  the  factors  whose  opera- 
tions will  produce  it  are  known.  Moisture  causes 
plants  to  grow  when  it  is  combined  in  the  proper  pro- 
portion with  heat  and  sunshine  and  good  soil.  It  is 
evident  that  quantities  are  important  if  we  are  to  pre- 
dict. Thus,  we  must  have  knowledge  of  the  essential 
conditions,  qualitative  and  quantitative,  of  an  event 
and  have  assurance  of  their  presence  before  we  have 
the  logical  right  to  predict  an  event  with  certainty.  In 
a  carefully  conducted  experiment  in  chemistry  where 
quantities  and  qualities  are  both  under  control,  expec- 
tation is  based  on  exact  knowledge,  and  all  that  we  need 
to  assume  is  the  general  principle  of  the  Uniformity  of 
Nature.  Again,  prediction  is  possible  in  astronomy 
where  the  forces  at  work  are  relatively  few  in  number 
and  measurable.  In  this  realm  of  giant  masses  and  gravi- 
tational forces  acting  according  to  well-known  laws,  it 
is  possible  to  foretell  the  relative  positions  of  bodies 
and  so  arrange  in  tables,  centuries  ahead  or  behind  the 
present,  those  eclipses  and  juxtapositions  which  are  of 
human  interest.  But  when  the  antecedents  cannot  be 
analyzed  in  this  fashion  and  are  known  to  be  more 
fluctuating  in  their  permutations  and  combinations, 
prediction  loses  certainty  and  drops  to  probability. 

The   Meaning   of  Probability.     Probability  at- 


PROBABILITY  241 

taclies  to  particular  facts  and  to  generalizations.  We 
use  the  term  when  we  feel  that  the  balance  of  evidence 
is  in  favor  of  a  principle  or  an  indiAridual  fact  even 
though  it  has  not  been  raised  above  reasonable  doubt. 
So  far  as  principles  are  concerned,  their  probability  re- 
flects the  degree  to  which  they  are  supported  by  the 
collected  evidence.  It  may  be  that  all  the  evidence 
thus  far  attained  is  favorable  but  that  we  do  not  re- 
gard it  as  extensive  enough ;  or  it  may  be  that  the  evi- 
dence is  conflicting.  When  we  are  concerned  with  the 
probability  of  the  occurrence  of  an  event,  on  the  other 
hand,  we  are  attempting  to  make  an  estimate  of  our 
admittedly  insufficient  knowledge  to  determine  whether 
it  is  in  favor  of,  or  against,  this  particular  occurrence. 
We  temper  the  degree  of  our  expectation  in  accordance 
with  such  relevant  knowledge  as  we  can  gather.  In 
contrast  with  certainty,  we  may  say  that  probability  is 
the  degree  of  expectation  which  is  judged  to  be  war- 
ranted by  the  facts.  We  say  that  an  event  is  probable, 
or  quite  probable,  or  very  probable,  or  extremely 
probable. 

Probability  and  Chance.  Probability  must  not 
be  confused  with  objective  chance.  The  principle  of  the 
Uniformity  of  Nature  is  essentially  the  denial  of  any- 
thing like  real  chance  in  the  world.  But  nature  is  so 
complex  that  we  are  not  able  to  note  and  analyze  all 
the  conditions  of  the  majority  of  events.  Causal  fac- 
tors reinforce  and  counteract  one  another  in  unforeseen 
ways,  and  the  actual  result  can  be  learned  only  from 
experience.  That  I  turned  up  an  ace  of  spades  the  last 
time  I  cut  for  the  deal  was,  so  far  as  my  knowledge 
went,  a  case  of  chance.    In  short,  chance  is  a  term  ex- 


24«  THE  ESSENTIALS  OF  LOGIC 

pressive  of  my  ignorance  of  what  is  taking  place. 
"  There  is  no  doubt  in  lightning,"  writes  Jevons,  "  as 
to  the  point  it  shall  strike ;  in  the  greatest  storm  there 
is  nothing  capricious;  not  a  grain  of  sand  lies  upon 
the  beach  but  infinite  knowledge  would  account  for  its 
lying  there ;  and  the  course  of  every  falling  leaf  is 
guided  by  the  same  principles  of  mechanics  as  rule 
the  motions  of  the  heavenly  bodies."  ^ 

Three  Kinds  of  Estimations.  Eoughly  speaking, 
we  may  distinguish  three  kinds  of  probability-estima- 
tions. The  first  is  empirical  and  largely  qualitative; 
the  second  deals  with  averages  and  is  closely  connected 
with  the  development  of  statistics ;  the  third  is  of  a  de- 
ductive, mathematical  type.  What  logic  is  interested 
in  is  the  nature  of  the  induction  and  the  dangers 
run. 

Empirical,  or  Non-Quantitative,  Probability. 
As  regards  most  events,  we  do  not  keep  any  exact  record 
of  how  things  have  happened  in  the  past,  but  trust 
to  a  general  impression,  to  a  sort  of  cumulative  esti- 
mation expressive  of  past  experience.  This  judgment 
is  then  related  to  the  particular  circumstances  of  the 
case  in  hand  and  a  feehng  of  probability  arises  in  con- 
sciousness. Suppose  that  you  hear  that  a  person  whose 
name  is  not  given  has  met  with  an  accident  in  the  city 
of  Washington.  The  idea  may  come  to  you  that  it  may 
be  your  brother  who  lives  there ;  but  the  idea  is  sure 
to  be  dismissed  unless  other  information  points  in  the 
same  direction.  Suppose  that  the  accident  happens  in 
a  government  building  where  he  works,  and  that  the 
description  of  the  individual  tallies  somewhat  with  his 
*  Principles  of  Science,  vol.  i,  p.  225. 


PROBABILITY  243 

appearance,  your  passing  idea  begins  to  be  entertained 
more  seriously  and  you  await  some  letter  or  telegram. 
If  it  does  not  come  within  a  day  or  so,  you  dismiss  the 
suggestion.  You  know  that  there  are  many  govern- 
ment employees  and  that  rough  descriptions  apply  to 
large  numbers  of  individuals  equally  well. 

Probabilities  based  on  Averages.  A  frequently 
employed  method  of  calculating  probabilities  is  the 
study  of  averages  for  classes.  Sometimes  such  a  study 
is  non-statistical,  but  it  readily  passes  into  the  stage  of 
statistics.  An  individual  may  calculate  that  he  has  many 
more  years  to  live  because  he  is  healthy  and  fairly 
young  and  is  working  in  a  profession  where  the  risks 
are  small.  "  This  type  of  reasoning  is  duplicated  in 
many  other  instances.  When  we  mail  a  letter,  we 
count  pretty  confidently  upon  its  safe  arrival.  From 
time  to  time,  letters  get  lost,  through  carelessness,  in 
railroad  wrecks,  or  as  a  result  of  other  causes,  but  the 
number  of  those  is  so  small  a  proportion  of  the  total 
number  that  we  treat  it  as  practically  a  negligible 
quantity.  For  the  same  reason  we  leave  out  of  account 
the  possibility  that  at  some  time  we  shall  be  struck  by 
lightning,  or,  when  we  make  a  journey,  that  our  train 
will  be  wrecked,  or  that  our  home  will  be  destroyed  by 
an  earthquake,  or  that  a  stranger  of  whom  we  make 
inquiries  as  to  directions  will  be  insolent  or  show  an- 
noyance." 1 

The  best  familiar  example  of  the  calculation  of  prob- 
abilities for  a  class  is  to  be  found  in  the  field  of  life  in- 
surance. Tables  are  worked  out  for  the  various  trades 
and  professions  and  for  individuals  of  different  ages. 
^  Bode,  An  Outline  of  Logic,  p.  150. 


244  THE  ESSENTIALS  OF  LOGIC 

Any  applicant  is  classified  and  his  probable  length  of 
life  estimated  by  reference  to  the  group  in  which  he  is 
classified.  A  danger  of  fallacy  lurks  in  this  method 
when  its  meaning  is  misunderstood.  It  must  be  borne 
in  mind  that  such  probability  only  applies  to  the  class 
and  not  directly  to  the  individual.  We  are  not  able  to 
predict  which  individuals  will  die,  but  only  that  about 
so  many  out  of  every  thousand  of  a  certain  age  will  die. 
It  is  upon  the  constancy  of  these  averages  that  the  com- 
pany calculates  the  necessary  premium. 

Estimates  of  'probability  are  made  more  accurate  hy 
deepening  the  classifications  made.  The  greater  the 
number  of  essential  characteristics  that  are  included, 
the  smaller  and  more  homogeneous  the  class.  Thus, 
teachers  and  ministers  are  known  to  have  a  far  longer 
average  of  life  than  miners  and  textile  workers.  Statis- 
tics have  shown  that  the  average  length  of  life  of  the 
rich  is  greater  than  that  of  the  poor.  It  has  been  esti- 
mated that  in  England  the  average  duration  of  life 
among  the  wealthy  classes  is  from  fifty-five  to  fifty-six 
years,  while  in  the  working  classes  it  falls  to  twenty- 
eight  years,  or  even  lower. 

A  word  of  warning  may,  perhaps,  be  advisable  at 
this  point.  Probability  of  this  objective  sort  is  based 
on  the  use  of  statistics.  Now  the  growth  of  statistics 
has  shown  a  constancy  in  the  number  of  crimes  com- 
mitted in  a  certain  country  in  the  course  of  a  year,  in 
the  number  of  suicides,  in  the  number  of  fires,  etc. 
In  the  preceding  chapter,  we  spoke  of  this  regularity  as 
the  *  law  of  inertia  of  large  numbers.'  Tlie  meaning  of 
this  law  has  been  much  misunderstood,  many  fearing 
that  it  implied  a  kind  of  mechanical  necessity  at  work 


PROBABILITY  245 

in  society  corresponding  to  the  'reign  of  law  '  in  nature. 
It  is  well  to  bear  in  mind  that  such  expressions  are 
metaphorical  and  that  we  must  penetrate  behind  them 
to  the  exact  facts  of  the  case.  Laws  are  human  formu- 
lations and  do  not  reign  in  the  physical  world  by  divine 
right  or  otherwise.  In  the  same  way,  statistical  constan- 
cies are  only  formulations  of  data  and  do  not  imply  any 
fate  lying  back  of,  and  controlling,  society.  The  follow- 
ing passage  from  Quetelet,  the  famous  Belgian  statis- 
tician, is  worth  quoting  in  this  connection  :  "  Amongst 
the  facts  disclosed  in  my  book,  the  one  which  has  given 
rise  to  most  alarm  is  the  constancy  of  crime  from  year 
to  year.  By  a  comparison  of  numbers,  I  believed  I  had 
data  for  inferring,  as  a  natural  consequence,  that  in  a 
given  country,  under  the  same  conditions  and  influ- 
ences, we  might  expect  a  repetition  of  the  same  facts, 
a  reproduction  of  the  same  crimes  and  the  same  con- 
demnations. But  how  was  this  received?  A  crowd  of 
timid  people  raised  the  cry  of  fatalism !  Now,  what  do 
the  facts  teach  us  ?  This,  simply,  —  that  in  any  given 
state,  subject  to  the  influence  of  the  same  causes,  the 
effects  will  not  differ  appreciably ;  they  will  oscillate 
more  or  less  about  some  mean.  Now,  mark  what  I  have 
said :  subject  to  the  influence  of  the  same  causes ;  so 
that,  therefore,  if  those  causes  change,  the  effects  will 
be  likewise  modified.  But,  since  the  laws  and  principles 
of  religion  and  morality  are  the  source  of  the  influences 
in  question,  I  cherish  not  only  the  hope,  but  —  what 
you  perhaps  do  not  —  the  deepest  conviction  even,  that 
society  can  be  reformed  and  ameliorated."  The  clear- 
sighted student  will  realize  that  we  are  here  skirting 
some  of  the  most  interesting  problems  of  philosophy. 


246  THE  ESSENTIALS  OF  LOGIC 

What  it  is  important  and  easy  to  realize  is  that  con- 
stancy in  averages  does  not  involve  fatalism. 

The  Mathematical  Treatment  of  Probability. 
We  can  divide  the  mathematical  treatment  of  probabil- 
ity into  two  parts,  the  conditions  for  the  application  of 
a  calculus  of  probability  and  the  rules  for  estimating 
probability. 

The  first  condition  for  the  application  of  a  calculus 
of  probability  to  events  is  the  possession  of  knowledge 
sufficient  to  assure  us  that  some  one  or  other  of  a  defi- 
nite number  of  ways  of  happening  are  possible,  but  not 
sufficient  to  inform  us  in  which  particular  way  the  event 
will  occur.  There  must  be  this  peculiar  mixture  of 
knowledge  and  ignorance.  "  For  example,  if  a  penny  is 
tossed  it  will  fall  with  either  head  or  tail  uppermost. 
Now,  which  will  be  uppermost  in  any  particular  throw 
will  be  exactly  determined  by  such  conditions  as  the 
position  of  the  coin  at  starting,  how  it  is  grasped  in  the 
fingers,  the  force  and  direction  of  the  twist,  etc.  But 
what  special  form  these  conditions  wiU  take  we  are  to- 
tally ignorant."^  The  second  condition  is  that  the  same 
general  set  of  conditions  and  antecedents  must  be  pres- 
ent and  operative  during  the  whole  course  of  the  events 
for  which  a  calculation  is  being  made.  For  instance,  to 
substitute  another  coin  with  a  curve  on  one  of  its  sur- 
faces for  the  original  one  would  make  a  calculation  im- 
possible. Both  of  these  conditions  are  secured  in  games 
of  chance.  Since  it  is  not  the  function  of  the  logician 
to  enter  into  the  mathematics  of  probability  in  detail 
but  only  into  the  logical  theory  at  its  foundation,  we 
shall  consider  only  the  simplest  cases. 

*  WeltoD,  Manual  of  Logic,  vol.  n,  p.  167. 


PROBABILITY  247 

The  probability  of  a  single  event  is  expressed  by  a 
fraction  whose  numerator  is  the  number  of  favorable 
alternatives,  and  denominator  the  total  number  of  al- 
ternatives. Since  a  coin  has  only  two  sides,  the  proba- 
bility of  getting  heads  in  any  one  trial  is  |.  We  say 
that  the  chances  for  heads  and  tails  are  equal  and  that 
the  probability  of  each  is  ^.  In  the  case  of  dice,  the 
number  of  sides  is  greater  and,  accordingly,  the  prob- 
ability for  any  one  side  is  less.  The  denominator  is  6 
while  the  numerator  is  1  for  any  one  side.  This  is  ex- 
pressed in  mathematical  form  by  saying  that  the  prob- 
ability for  each  side  is  ^.  The  method  of  reasoning  in  the 
case  of  playing  cards  is  essentially  the  same.  The  total 
number  of  possibilities  is  52  and  the  chance  for  any  one 
card  is  -^^.  The  chance  of  getting  an  ace  would  be  -^. 

There  are  two  rules  with  compound  events  according 
as  such  events  are  (1)  independent  or  (2)  dependent 
o^  one  another. 

J%e  probability  of  obtaining  any  combination  of  in- 
dependent events  is  the  product  of  the  probabilities  of 
the  several  events.  Let  us  take  the  throwing  of  dice  as 
an  example.  "  If  one  die  is  thrown  the  probability 
that  it  will  fall  with  the  side  bearing  six  pips  upper- 
most is  ^,  as  the  die  has  six  sides,  and  the  probability 
of  being  uppermost  is  equal  for  them  all.  If  a  second 
die  is  thrown  the  probability  that  in  that  throw  six  will 
be  uppermost  is  also  ^ ;  consequently  the  probability 
that  six  will  be  thrown  in  each  of  two  throws  is  i  X  |  =  ■^^. 
In  this  case,  it  is  obviously  immaterial  whether  two  dice 
are  thrown  simultaneously  or  whether  the  same  die  is 
thrown  successively."  ^  Obviously  the  number  of  pos- 
1  Welton,  Manual  of  Logic,  p.  174. 


248  THE  ESSENTIALS  OF  LOGIC 

sibilities  is  36  and  only  one  of  these  is  the  combination 
desired. 

If  two  events  are  mutually  exclusive,  the  probability 
of  getting  one  or  the  other  is  the  sum  of  their  inde- 
pendent probabilities.  Thus,  in  throwing  dice,  the 
probability  of  getting  a  six  or  a  five  is  ^  +  ^»  ©^  ^.  The 
principle  is  the  same  as  for  simple  events. 

We  come  now  to  compound  events  in  which  the 
occurrence  of  the  first  affects  the  probability  of  the 
occurrence  of  the  others.  In  such  cases  the  probability 
of  the  compound  event  is  the  product  of  the  probability 
of  the  first  with  the  probability  of  the  second  as  af 
fected  by  the  first.  "For  example,  what  is  the  proba- 
bility of  drawing  two  white  balls  in  succession,  without 
replacing  the  first  drawn,  from  an  urn  containing  two 
white  balls  and  one  black  one  ?  If  a  black  is  drawn 
first,  the  estimate  is  rendered  impossible.  The  proba- 
bility of  drawing  a  white  first  is  |.  If  it  is  drawn,  the 
constitution  of  the  urn  for  the  second  draw  is  modified 
by  the  first  draw.  There  are  now  only  two  balls,  one 
white  and  one  black,  in  the  urn  ;  and  the  probability  of 
drawing  the  white  is  ^."  Therefore,  the  probability  of 
drawing  two  whites  is  |^  X  ^  =  ^. 

Mistakes  in  interpreting  Probabilities.  Mis- 
takes are  often  made  in  the  interpretation  of  probabili- 
ties. Probabilities  based  on  averages,  as  in  life  insur- 
ance, do  not  give  us  any  information  in  regard  to  any 
particular  individual.  "  Statistics,  from  the  very  nature 
of  the  subject,  cannot  and  never  will  be  able  to  take 
into  account  individual  cases."  ^  When  we  come  to  de- 
ductive, or  mathematical,  probability,  other  warnings 
^  King,  Elements  of  Statistics,  p.  86. 


PROBABILITY  249 

must  be  issued,  especially  for  the  non-mathematician. 
He  must  bear  the  above  rules  in  mind  and  remember, 
for  instance,  that  the  throws  "  in  which  we  get  a  six 
with  either  of  two  dice  are  not  so  common  as  the  throws 
in  which  we  get  either  a  six  or  an  ace  with  one  die. 
We  turn  up  as  many  sixes  with  the  two  dice  as  we  turn 
up  sixes  and  aces  with  one ;  but  since  the  two  sixes  are 
on  different  dice  and  are  therefore  not  incompatible, 
they  come  together  in  one  throw  out  of  thirty-six,  and 
we  do  not  turn  them  up  in  so  many  separate  throws."  ^ 
Another  point  is  of  interest.  The  past  run  of  throws 
can  offer  no  basis  for  an  inference  as  to  the  character 
of  the  next  throw.  "  To  expect  that,  because  a  coin  has 
come  up  heads  several  times  in  succession,  it  is  there- 
fore more  likely  to  come  up  tails  the  next  time,  is 
wholly  to  misunderstand  the  meaning  of  probability. 
Indeed,  a  preponderance  of  heads  in  the  past  throws 
would  suggest  that  the  coin  was  not  true,  that  there  was 
a  hidden  cause  favoring  heads,  and  that  as  a  matter  of 
fact  the  probability  of  heads  was  greater  than  one 
half."  2  We  see,  then,  that  the  calculus  of  probability 
is  only  a  guide  which  we  take  when  we  cannot  secure 
definite  information  about  particular  cases.  Moreover, 
it  is  only  when  certain  conditions  are  fulfilled  that  the 
probability  in  favor  of  a  certain  occurrence  can  be  esti- 
mated with  any  large  degree  of  mathematical  accuracy. 

^  Aikins,  The  Principles  of  Logic,  p.  340. 

*  Jones,  Logic  Inductive  and  Deductive,  p.  223. 


250  THE  ESSENTIALS  OF  LOGIC 


REFERENCES 

Aikins,  The  Principles  of  Logic,  chap.  xxxn. 
Bode,  An  Outline  of  Logic,  chap.  xi. 
CofiEey,  The  Science  of  Logic,  vol.  ii,  p.  v,  chap.  n. 
Jones,  Logic,  Inductive  and  Deductive,  pt.  ii,  chap.  m. 
Welton,  Manual  of  Logic,  bk.  v,  chap.  vi. 


CHAPTER  XXII 

AVERAGES  AND  GRAPHS 

The  Uses  of  Averages.  In  the  two  preceding  chap- 
ters we  have  had  frequent  occasion  to  speak  of  aver- 
ages. Statistics  does  not  concern  itself  with  the  individual 
case,  but  with  the  average  for  a  group  or  collection. 
Thus,  we  are  presented  with  the  average  income  per 
capita^  the  average  number  of  rooms  in  the  houses  oc- 
cupied by  working  people,  the  typical  expenditure  of  a 
family  for  food,  etc.  Insurance,  industrial,  and  health 
statistics  all  take  this  form.  It  behooves  us,  therefore, 
to  have  some  knowledge  of  the  methods  used  in  obtain- 
ing such  averages  and  the  ways  in  which  they  are  best 
presented  to  the  mind. 

The  following  uses  summarize  very  well  the  view  of 
the  modern  investigator :  — 

"  Averages  are  used :  1.  To  give  a  concise  picture 
of  a  large  group.  We  could  not  grasp  the  idea  well 
if  given  the  height  of  every  tree  in  a  forest,  but  the 
average  height  is  something  definite  and  comprehen- 
sible. 

"  2.  To  compare  different  groups  hy  means  of  these 
simple  pictures.  Thus,  two  forests  can  only  be  com- 
pared by  means  of  totals  or  averages  of  some  sort. 

"  3.  To  obtain  a  picture  of  a  complete  group  hy  the 
use  of  sample  data  only.  An  average  obtained  from  a 
few  hundred  samples  is  so  close  to  the  exact  average  of 
the  whole  that  the  difference  is  negligible. 


252  THE  ESSENTIALS  OF  LOGIC 

"  4.  To  give  a  mathematical  concept  to  the  relation- 
ship between  different  groups.  We  may  say  that  the 
trees  in  one  forest  are  taller  than  in  another,  but  in 
order  to  find  any  definite  ratio  of  heights,  it  is  neces- 
sary to  resort  to  averages."  ^ 

The  logic  of  such  a  situation  is  clear.  In  statistics, 
we  stress  the  quantitative  or  measurable  side  of  things  ; 
and  we  take  them,  not  as  individuals,  but  as  groups. 
The  only  way  to  institute  a  comparison  is  to  reduce 
them  to  some  common  unit.  What  this  common  unit 
will  be  depends  largely  upon  the  purpose.  We  shall 
briefly  describe  the  common  averages  used  and  point 
out  their  special  value. 

The  Arithmetical  Average.  The  arithmetical 
average  is  the  sum  of  the  particular  items  divided  by 
their  number.  By  means  of  such  an  average,  we  are 
able  to  handle  all  the  items  as  a  single  typical  unit 
which  we  are  able  to  compare  with  other  like  units. 
Thus,  two  football  teams  may  be  compared  in  regard 
to  their  weight  by  this  means.  Suppose  the  weights  of 
the  members  of  one  team  were  162,  180,  190,  155, 
170,  176,  182,  167,  205,  169,  158  pounds;  then 
the  average  weight  would  be  174  pounds.  The  same 
method  would  be  used  to  determine  the  average  for  the 
other  team,  and  so  a  comparison  could  be  instituted. 

It  is  obvious  that  such  information  as  the  above  has 
its  limitations.  It  makes  a  deal  of  difference  where  the 
weight  in  a  team  is  distributed,  and  a  general  average 
for  the  whole  group  does  not  bring  this  out.  Hence 
smaller  groups  are  taken,  such  as  the  backfield  or  the 
line,  and  further  comparisons  instituted.  The  advan- 
^  King,  Elements  of  Statistics,  p.  121. 


AVERAGES  AND  GRAPHS  253 

tages  and  disadvantages  of  the  arithmetical  average 
will  be  discussed  later. 

The  'Weighted'  Average.  "By  a  'weighted' 
average,  we  mean  one  whose  constituent  items  have 
been  multiplied  by  certain  weights  before  being  added, 
the  sum  thus  obtained  being  divided  by  the  sum  of  the 
weights  instead  of  by  the  number  of  items."  There  are 
two  types  of  weighted  averages :  one  in  which  groups 
with  varying  numbers  of  members  are  already  averaged 
and  we  desire  to  secure  the  arithmetical  average  for  the 
groups  taken  together ;  and  the  other  in  which  the 
weights  stand  for  estimates  of  relative  importance. 

An  example  will  make  the  first  type  clear.  If,  for 
example,  a  department  store  had  seven  departments 
and  the  average  wage  for  each  department  was  known, 
to  obtain  the  weighted  average  it  would  be  necessary 
to  multiply  the  average  wage  for  each  department  by 
the  number  of  workers  in  it,  add  the  results  together, 
and  divide  by  the  total  number  of  workers. 

The  second  type  appears  in  the  use  of  '  index-num- 
bers '  which  represent  the  estimated  importance  of  the 
various  groups.  The  following  discussion  by  Bowley 
brings  out  very  well  the  nature  of  the  problem  and  the 
way  in  which  it  is  met :  — 

The  classical  and  most  useful  application  of  weights 
is  the  formation  of  an  index-number  for  the  change  of 
prices  by  fitting  suitable  weights  to  the  changes  meas- 
ured in  the  prices  of  various  commodities.  It  is  re- 
quired to  find  the  change  in  the  value  of  gold  when 
measured  by  the  prices  of  other  commodities.  Suppose 
that  we  are  given  that  prices  of  certain  commodities 
between  two  years  were  in  the  following  ratios :  — 


254  THE  ESSENTIALS  OF  LOGIC 

Wheat      Silver      Meat      Sugar      Cotton 

First  year 100        100        100        100        100 

Second  year 77  60  90  40  85 

The  simplest  way  to  estimate  for  the  general  fall 
in  price  is  to  take  the  simple  average  of  the  numbers 
in  the  second  year,  viz.,  70.4,  and  say  that  the  general 
prices  in  the  second  year  were  70.4  :  100  when  ex- 
pressed in  commodities.  But  it  is  at  once  clear  that  we 
cannot  allow  the  commodities  given  to  have  equal  influ- 
ences on  the  result;  wheat  is  of  greater  importance 
than  sugar  and  meat  than  silver;  and  again,  we  have 
taken  arbitrarily  three  items  to  represent  food  and  one 
for  clothing;  we  need  some  means  of  deciding  relative 
importance.  Suppose  we  decide  that  wheat,  cotton, 
meat,  and  sugar  are  respectively  7,  4,  3  times  and 
twice  as  important  as  silver,  we  should  get  the  follow- 
ing table  :  — 

Commodity  Belative  prices  in  Weight  p^ 

"  second  year  assigned 

Wheat '..  77  7  639 

Silver 60  1  60 

Meat 90  3  270 

Sugar 40  2  80 

Cotton _86  _4  340 

352  17  1289 

1289 
Weighted  average  is ... . =  75.8 

352 

Unweighted  average  is. . =  70.4* 

6 

Weights  are  expressions  of  expert  judgment  and  are 
to  a  certain  extent  relative.  The  logician  must  recog- 
nize that  a  possibility  of  error  lies  in  their  assignment. 

^  Bowley,  Elements  of  Statistics,  pp.  111-12,  quoted  from  Jones. 


AVERAGES  AND  GRAPHS  255 

Fortunately,  it  can  be  demonstrated  that  an  error  in 
weights  is  less  serious  in  its  effects  than  a  mistake  in 
the  size  of  the  original  items. 

The  Mode.  Another  average  which  is  very  useful 
is  the  mode.  It  is  variously  defined  as  the  most  fre- 
quent size  of  item,  the  positions  of  greatest  density,  and 
the  quantity  which  occurs  with  the  greatest  frequency. 
It  is  what  we  usually  have  in  mind  when  we  speak  of 
*  the  average  man,'  '  the  average  income,'  '  the  average 
sized  apple,'  etc.  We  may  say  that  the  mode  represents 
the  type. 

The  mode  is  not  always  easily  determinable.  When 
the  case  is  simple,  the  mode  can  be  determined  by  an 
examination  of  a  frequency  table.  The  following  exam- 
ple should  make  the  method  clear  :  — 

Frequency  Table  shotoing  Heights  of  Cornstalks 


'i,  (size  of  item) 

No.  of  stalks  {frequency) 

m 

f 

3-4 

3 

4-5 

7 

&-6 

il2 

6-7 

60 

7-8 

85 

8-9 

S& 

9-10 

8 

n  =  217 

It  will  be  noticed  that  size  7-8  is  found  85  times, 
which  is  the  greatest  frequency,  and  is  therefore  the 
mode.  There  may  be  two  or  more  frequencies  with 
about  equal  claims  to  be  the  most  usual  occurrence. 
Such  is  the  case  in  the  variations  of  animal  forms  where 
one  type  shades  continuously  over  into  another.  The 


256  THE  ESSENTIALS  OF  LOGIC 

finer  the  grades,  the  easier  it  is  to  determine  the  domi- 
nant mode. 

The  value  of  the  mode  comes  out  in  the  following 
examples :  "  The  mode  rather  than  the  average  in  chest- 
measurements  is  the  number  most  suitable  for  the 
ready-made  clothier.  For  providing  a  post-office  or  a 
store,  the  mode  in  postal-orders  or  prices  of  tea  needs 
to  be  known  rather  than  any  other  average.  Even  the 
favorite  coin  in  a  collection  may  show  the  spirit  of  the 
congregation  better  than  the  arithmetic  average  of  their 
contributions." 

The  Median.  The  median  is  the  middle  quantity  in 
a  series.  "  If  a  number  of  similar  objects  are  placed 
side  by  side  in  order  of  their  size,  they  are  said  to  be 
arrayed.  If  any  group  of  objects  is  thus  arrayed,  the 
middle  one  is  known  as  the  median  item." 

The  median  is  of  particular  value  when  the  data 
dealt  with  are  not  susceptible  of  measurement  in  defi- 
nite units.  Psychological  phenomena  come  in  this  class 
of  material.  "  It  is  impossible  to  measure  in  specific 
units  the  mental  characteristics  of  a  child  but  it  is  per- 
fectly possible  to  array  a  group  of  children  according 
to  their  respective  mentality."  ^  For  this  reason,  the 
median  was  used  by  Francis  Galton  in  his  investiga- 
tions in  inheritance  and  is  being  used  in  fields  where 
quality  can  be  graded  in  a  series. 

The  G-eometric  Average.  The  geometric  average 
is  obtained  by  multiplication  of  the  n  items  of  a  series, 
and  the  extraction  of  the  nth  root  of  the  produce.  This 
average  soon  reaches  a  complexity  which  makes  it  im- 
possible of  easy  application  for  those  not  familiar  with 

^  King,  Elements  of  Statistics,  p.  131. 


AVERAGES  AND  GRAPHS  257 

mathematics.  Beyond  the  square  and  cube  root,  it  in- 
volves the  use  of  logarithms.  It  is  very  little  used  at 
the  present.  % 

The  Comparative  Advantages  of  these  Aver- 
ages. The  mode  is  of  advantage  where  we  are  not  con- 
cerned with  extreme  variations  which  are  few  in  num- 
ber, but  with  the  type.  Its  disadvantage  is  that  it  is 
not  always  easy  to  determine.  The  median  is  easily  lo- 
cated and  can  be  determined  for  all  data  which  can  be 
arrayed  in  a  series.  Its  chief  advantage  is  that  it  is  ap- 
plicable to  relatively  qualitative  fields.  The  arithmetical 
average  is  readily  calculated  and  gives  weight  to  all  the 
items ;  its  chief  disadvantage  is  that  it  requires  the 
presence  of  all  the  items  and  even  emphasizes  the  ex- 
tremes. The  weighted  average  is  a  correction  of  the 
arithmetical  when  the  series  is  made  up  of  groups ;  its 
chief  importance,  however,  lies  in  its  adaptation  to  the 
use  of  index-numbers.  The  average  used  in  any  con- 
crete investigation  is  determined  by  the  character  of 
the  problem  and  the  nature  of  the  material.  Often  more 
than  one  average  is  calculated. 

Graphs  and  Graphical  Methods.  Diagrams  are 
often  employed  to  summarize  tables  in  a  picturesque 
and  striking  way.  Various  devices  have  been  worked 
out  to  render  the  meaning  of  masses  of  figures  clear 
and  unambiguous.  The  following  simple  diagrams  are 
often  used  in  the  exposition  of  statistical  data :  — 

1.  Cartograms.  Phenomena  with  a  geographical 
location  can  be  brought  clearly  before  the  eye  by  means 
of  maps  with  devices  to  show  variations.  Colored  print- 
ing is  sometimes  used,  but,  since  this  is  expensive,  va- 
rious modes  of  barring  are  employed.  The  rainfall  maps 


258  THE  ESSENTIALS  OF  LOGIC 

printed  in  the  newspapers  are  good  examples  of  this 
class.  Another  method  is  the  use  of  dots  to  indicate  the 
relative  amount  of  the  product  under  investigation, 
each  dot  standing  for  a  given  quantity.  Such  things  as 
wheat  and  corn  production  can  be  represented  in  this 
way  so  that  the  results  appeal  directly  to  the  eye. 

2.  Pictograms.  Pictures  of  comparative  sizes,  bar 
diagrams,  block  pictograms,  and  circles  divided  into 
segments  are  some  of  the  devices  used  to  bring  data 
before  the  eye.  The  importance  of  such  pictorial  meth- 
ods for  exposition  can  hardly  be  overestimated.  "After 
a  person  has  collected  data  and  studied  a  proposition 
with  great  care  so  that  his  own  mind  is  made  up  as  to 
the  best  solution  for  the  problem,  he  is  apt  to  feel  that 
his  work  is  about  completed.  Usually,  however,  when 
his  own  mind  is  made  up,  his  task  is  only  half  done. 
The  larger  and  more  difficult  part  of  the  work  is  to 
convince  the  minds  of  others  that  the  proposed  solution 
is  the  best  one  —  that  all  the  recommendations  are 
really  necessary."  ^  One  of  the  advantages  of  the 
graphic  method  is  that  the  facts  can  be  so  presented 
that  the  reader  can  make  deductions  of  his  own. 

Experience  has  shown  that  some  forms  of  charts  are 
far  superior  to  others  and  that  faulty  arrangements  are 
easily  adopted  when  criticism  has  not  been  directed 
against  them.  The  bar  method  has  many  advantages 
in  that  it  permits  an  exact  estimation  of  the  component 
parts  and  the  use  of  colors  to  distinguish  them.  A 
development  of  the  bar  method  by  subdivision  bars  is 
shown  in  Fig.  15.^  The  sector  method  is  widely  used  in 

'  Brinton,  Graphic  Methods  for  Presenting  Facts,  p.  1. 

^  Figures  15, 16,  and  17,  on  pages  259,  260,  261,  are  taken  from  Brin- 
ton's  Graphic  Methods/or  Presenting  Facts,  by  permission  of  the  pub- 
lishers, The  Engineering  Magazine. 


^1  A 

ll   ll 


^  s 


ta     ^ 


260 


THE  ESSENTIALS  OF  LOGIC 


popular  magazines ;  its  disadvantage  lies  in  its  lack  of 
flexibility  and  the  difficulty  of  arranging  and  lettering 
the  sectors  of  the  circle.  Fig.  16,  taken  from  The 
Survey^  is  a  good  example  of  pictorial  presentation. 

In  almost  every  chapter  we  have  been  compelled  to 
stress  the  importance  of  analysis  for  thinking.  What 
is  called  '  scientific  management '  is  beginning  to  point 
out  its  importance  for  social  and  industrial  fields.  The 
way  in  which  the  graphic  method  is  being  employed 
for  this  purpose  is  shown  in  Fig.  17,  taken  from  System. 


FlO.  16.  DISPOSITION  OF  A   FAMILY   INCOME  OF  FROM 
$900  TO  £1000 

This  cut  Bhowg  an  attempt  to  put  figures  in  popular  form.    The  eye  is  likely 
to  judge  by  the  size  of  the  pictures  rather  than  by  the  angles  of  the  sectors. 


262  THE  ESSENTIALS  OF  LOGIC 

"Authority  reaches  down  through  the  several  branches 
of  an  organization  like  descent  of  blood,  and,  if  prop- 
erly planned,  it  will  be  as  irregular  for  a  factor  in  an 
organization  to  be  in  doubt  as  to  the  person  in  authority 
over  him  as  for  the  child  to  deny  the  parentage  of  his 
father.  ...  It  should  be  graphically  shown  what  posi- 
tions are  only  temporarily  filled,  so  that  when  new  men 
are  engaged  they  will  fit  into  the  scheme  with  functions 
planned."  ^  In  such  classification,  we  are  dealing  with 
parts  of  a  system  rather  than  with  genera  and  species 
as  in  natural  science. 

3.  Frequency  Graphs.  Frequency  tables  are  reduced 
to  graphs  in  various  ways.  The  foundation  is  the  em- 
ployment of  coordinates  cutting  each  other  at  right 
angles  at  a  point  called  the  '  origin.'  One  set  of  data 
is  measured  along  the  axis  of  abscissae,  while  the  other 
set  is  measured  along  the-ordinate.  A  line  drawn  through 
points  determined  in  this  way  is  called  a  'graph'  and 
shows  the  essential  points  of  the  table.  "  For  example, 
if  the  world's  production  of  wheat  over  a  number  of 
years  be  plotted,  a  poor  yield  is  represented  by  a  de- 
pression, a  rich  one  by  a  peak,  a  uniform  one  over 
several  years  by  a  horizontal  line,  and  so  on."  It  has 
been  found  that  graphs  dealing  with  different  cases  of 
the  same  phenomenon  can  be  plotted  on  the  same  co- 
ordinates and  so  compared.  Often  considerable  ingenu- 
ity is  demanded  before  the  graphs  assume  a  form  which 
lends  itself  to  comparison. 

*  Brinton,  Graphic  Methods  far  Preienting  Facts,  p.  16. 


AVERAGES  AND  GRAPHS        263 

REFERENCES 

Bowley,  Elements  of  Statistics. 

Brinton,  Graphic  Methods  for  Presenting  Facts. 

Davenport,  Statistical  Methods  with  Special  Reference  to  Biological 
Variation. 

Elderton,  Primer  of  Statistics. 

Jones,  Logic,  Inductive  and  Deductive,  pt.  ll,  chap,  n,  and  Sup- 
plement. 

King,  Elements  of  Statistics. 


CHAPTER  XXIII 

TESTIMONY  AND  CIRCUMSTANTIAL  EVIDENCE 

Scientific  Investigation  vs.  Judicial  Proof.  Thus 
far  we  have  largely  concerned  ourselves  with  the  meth- 
ods and  logical  processes  of  those  investigations  whose 
object  is  the  discovery  of  laws  and  principles.  Such 
investigations  are  essentially  impersonal  and  theoretical. 
They  can  be  carried  on  in  the  laboratory  and  the  study, 
and  there  is  usually  less  controversy  in  regard  to  the 
facts  than  in  regard  to  the  hypotheses  to  be  erected 
upon  them.  Many  seekers  in  the  same  field,  having 
much  the  same  training,  accumulate  facts  by  means  of 
critical  observation,  and  these  facts  are  to  furnish  the 
foundation  of  the  science.  These  accepted  facts  grad- 
ually converge  in  the  direction  of  some  satisfactory 
hypothesis,  and  so  a  law  of  nature  or  of  society  is  tenta- 
tively established.  We  see,  then,  that  science  is  coop- 
erative and  largely  impersonal,  its  data  can  be  increased 
by  recognized  methods  until  they  are  sufficient,  and  it 
is  not  limited  in  the  amount  of  time  at  its  disposal. 
Nature  is  besieged  rather  than  taken  by  storm.  How 
long  Newton  worked  before  he  published  his  results  is 
well  known,  but  it  is  not  so  well  known  that  Darwin 
worked  upon  the  development  of  his  theory  in  regard 
to  the  origin  of  species  for  more  than  twenty  years. 

But  there  is  another  great  field  of  systematic  reason- 
ing which  deserves  the  attention  of  the  logician.  If  the 
methods  and  temper  of  the  scientist  have  of  late  influ- 


CIRCUMSTANTIAL  EVIDENCE  265 

enced  the  popular  mind  in  the  direction  of  greater  care 
and  exactitude,  a  similar  influence  has  long  been  exerted 
by  the  methods  and  principles  of  legal  reasoning.  Sci- 
entific temper  is  paralleled  in  great  measure  by  judicial 
temper.  And  we  must  remember  that  the  situation  in 
which  legal  reasoning  is  carried  on  is  quite  different 
from  that  in  which  scientific  investigation  takes  place, 
and  is  much  less  favorable  to  good  reasoning.  The  air 
is  full  of  contention  and  of  the  personal  element,  the 
time  in  which  to  reach  a  decision  is  limited,  and  the 
necessary  facts  are  often  hard  to  find  and  verify.  Judi- 
cial proof  is  less  creative  than  scientific  investigation, 
but  it  is  in  many  ways  more  difficult. 

The  Difficulties  confronting  Judicial  Proof.  The 
difficulties  confronting  judicial  proof  are  very  similar 
to  those  which  arise  in  practical  life  when  the  problem 
is  controversial  in  character.  The  juror  is  not  in  a  posi- 
tion to  observe  the  facts,  but  must  reach  his  decision 
through  the  testimony  of  others  and  through  inference 
from  what  is  called  'circumstantial  evidence.'  The  sci- 
entific investigator  can  repeat  his  facts  at  wish,  but  this 
the  juror,  no  more  than  the  historian,  can  do.  "The 
same  combination  of  circumstances  which  go  to  make 
up  a  case  of  crime  cannot,  where  they  are  at  all  numer- 
ous, be  expected  to  occur  again.  And  even  if  it  could  or 
did  occur,  it  would  answer  no  purpose ;  for  it  is  the 
identical  transaction  which  took  place,  and  as  it  took 
place,  which  is  to  be  the  sole  subject  of  inquiry."  ^  The 
juror's  observation  is  of  an  indirect,  dependent,  and 
therefore  inferior  kind.  Again,  the  original  observer  of 
the  facts  was  seldom  aware  of  their  importance.  "  Many 
1  Burrill,  A  Treatise  on  Circumstantial  Evidence,  p.  94. 


266  THE  ESSENTIALS  OF  LOGIC 

of  the  facts  .  .  .  not  only  present  themselves  to  the 
senses,  incidentally,  unexpectedly,  and  transiently,  but 
are,  outwardly,  and  as  they  present  themselves,  of  the 
most  ordinary  and  familiar  kind,  having  nothing  on 
their  face  to  attract  or  arrest  attention  in  any  consider- 
able degree  ;  and  not  to  be  distinguished  from  the  great 
mass  of  facts  and  events  which  are  constantly  passing 
before  the  eyes  of  men,  in  their  daily  intercourse  with 
each  other.  Hence,  where  they  are  perceived  merely  by 
the  organs  of  sense,  without  any  act  on  the  part  of  the 
observer,  to  give  them  connection  with  himself,  they 
are  usually  perceived  in  a  general  and  superficial  man- 
ner." Thus,  there  is  a  large  amount  of  possible  error 
in  this  incomplete  and  indirect  observation  upon  which, 
as  a  foundation,  the  juror  must  build  his  construction 
of  the  case.  The  court  must  be  certain  of  the  identity 
of  the  witness  and  of  his  general  competency,  that  he 
was  actually  an  observer  of  what  he  testifies  to,  that 
his  testimony  is  not  biased,  etc.  Finally,  the  juror  must 
be  able  to  mass  all  this  evidence,  much  of  which  is  con- 
flicting, together  and  draw  a  conclusion  which  seems  to 
him  to  explain  the  facts  of  the  case.  He  is  compelled  to 
pass  judgment  after  judgment  and  then  to  estimate 
the  comparative  value  of  these  integral  yet  subordinate 
conclusions  in  a  total  view  of  the  problem.  Neither  the 
steps  nor  the  final  synthesis  is  easy  of  accomplishment 
in  complex  cases. 

Distinction  between  Circumstantial  and  Testi- 
monial Evidence.  All  evidence  involves  an  inference 
from  some  fact  to  the  proposition  to  be  proved.  To  be 
evidence,  a  fact  must  have  a  recognizable  bearing  upon 
the  issue  or  probandum.  In  such  a  bearing  lies  its  rel- 


CIRCUMSTANTIAL  EVIDENCE  267 

evance.  Evidence  divides  itself  into  two  classes,  called 
respectively ' direct'  or  '  testimonial  evidence  '  and  '  cir- 
cumstantial evidence.'  The  distinction  between  these 
two  types  is  as  follows  :  Direct  or  testimonial  evidence 
consists  of  information  derived  from  assertions  made 
hy  those  who  have  actual  knowledge  of  the  fact ;  cir- 
cumstantial evidence  consists  of  facts  from  which  in- 
ferences to  the  principal  fact  can  be  drawn.  Thus, 
testimonial  evidence  is  made  up  of  the  assertions  of 
witnesses  who  are  presumed  to  have  first-hand  knowledge 
of  the  fact  at  issue,  while  circumstantial  evidence  con- 
sists of  '  circumstances '  from  which  the  fact  at  issue 
can  be  inferred  according  to  known  laws.  It  must  be 
remembered,  however,  that  these  '  circumstances  '  must 
themselves  be  proved  by  testimony. 

The  Nature  of  Circumstantial  Evidence.  It  is 
obvious  that  circumstantial  evidence  gains  its  chief  im- 
portance as  supplementary  to  direct  evidence.  A  com- 
mon direction  for  these  two  kinds  of  evidence  is  almost 
bound  to  carry  conviction.  Thus,  there  may  be  only  one 
witness  who  testifies  to  having  seen  a  crime  committed, 
while  many  may  have  seen  the  accused  near  the  place 
and  showing  signs  of  agitation  or  marks  which  fit  in 
with  the  inference  suggested  by  the  prosecution.  Thus, 
testimonial  and  circumstantial  evidence  are  usually  in- 
tertwined. But  cases  occur  in  which  there  is  no  direct 
evidence,  i.e.,  in  which  no  one  has  witnessed  the  com- 
mission of  the  crime.  At  such  times,  reliance  must  be 
placed  wholly  upon  inference  from  circumstances.  For 
instance :  "  A  house  has  been  robbed.  All  the  property 
stolen  from  it  is  found  directly  after  the  robbery  in  the 
possession  of  A.    Besides  this,  at  the  time  when  the 


268  THE  ESSENTIALS  OF  LOGIC 

robbery  is  discovered,  a  hat,  usually  worn  by  A,  is  found 
in  the  house.  It  is  almost  certain  as  a  general  proposi- 
tion, that  any  man  of  whom  these  facts  are  true,  must 
be  the  robber.  And  assuming  it  to  be  conclusively 
established  that  both  these  facts  are  true  of  ^,  we  may 
conclude  with  an  approach  to  absolute  certainty  that  A 
is  guilty  of  the  robbery."  When  we  come  to  examine 
all  such  cases  of  circumstantial  evidence,  we  find  that 
the  principle  of  explanation  is  the  same  as  that  used  in 
science.  Given  certain  Jacts,  we  must  form  an  hypothe- 
sis to  explain  them.  In  a  case  like  the  above,  the 
hypothesis  that  A  is  the  robber  is  the  one  that  naturally 
occurs.  We  are  certain,  at  least,  that  if  he  is  not  the 
robber,  he  must  know  who  the  robber  is.  From  the 
standpoint  of  logic,  the  proof  of  the  hypothesis  consists 
in  the  elimination  of  all  alternative  possibilities.  The 
student  will  recall  that  Mill's  Methods  depended  largely 
upon  the  scientist's  ability  to  exclude  possible  causes 
and  so  narrow  down  the  field. 

The  Convergence  of  Evidence.  It  is  seldom  that 
a  single  circumstance  is  given  such  value  as  to  be  re- 
garded as  conclusive.  One  instance  occurred  which 
should  serve  to  put  us  on  our  guard  against  the  easy 
assumption  that  there  is  no  other  possible  hypothesis 
but  the  one  which  most  naturally  occurs  to  us.  "  A  man 
was  convicted  and  executed  for  stealing  a  horse,  on  the 
strength  of  the  presumption  of  the  animal's  being  found 
in  his  possession  on  the  same  day  on  which  it  was  stolen ; 
but  it  afterwards  appeared  that  the  real  thief,  being 
closely  pursued  by  the  officers  of  the  law,  had  met  the 
unfortunate  man,  to  whom  he  was  a  total  stranger,  and 
requested  him  to  walk  his  horse  for  him  for  a  while. 


CIRCUMSTANTIAL  EVIDENCE  269 

He  had  then  escaped."  In  practically  all  cases,  then, 
the  prosecution  builds  up  a  framework  of  evidence 
which  converges  on  the  hypothesis  that  the  accused  is  the 
guilty  man.  The  two  facts  to  be  connected  are  the 
crime  and  the  individual  charged  with  its  commission. 
The  evidentiary  facts  are  shown  to  converge  upon  such 
a  suggested  connection.  The  figure  most  frequently  em- 
ployed is  that  of  a  chain,  but  the  analogy  has  a  weak- 
ness so  far  as  it  implies  that  the  disproof  of  a  single 
link  will  break  the  chain.  As  a  matter  of  fact,  the  con- 
nection is  more  like  a  cable  woven  of  strands  than  a 
single  chain.  When  each  single  inference  from  a  circum- 
stance to  the  issue  is  probable,  the  combination  of  these 
separate  probabilities  may  lead  to  a  moral  certainty 
through  the  impossibility  of  finding  an  hypothesis,  other 
than  the  one  championed,  which  will  cover  them  all. 
The  defense  then  tries  to  break  down  the  framework 
of  evidence  by  trying  to  disprove  certain  of  the  alleged 
facts,  by  attempting  to  show  that  the  interpretation  of 
other  facts  is  false,  and,  in  short,  by  seeking  to  bring 
forward  another  hypothesis  as  an  explanation.  And  so 
the  struggle  between  the  two  sides  continues,  with  the 
jury  as  tlie  deciding  body. 

Direct  or  Testimonial  Evidence.  When  we  are 
dealing  with  past  events,  as  in  a  case  of  crime  and  in 
history,  we  are  compelled  to  rest  our  beliefs  upon  some 
sort  of  testimony.  Testimony,  if  true,  enables  us  to  reap 
the  results  of  the  perceptions  of  others,  to  see  indirectly 
with  their  eyes.  Hence,  testimony  has  an  unique  value. 
But  it  has  also  its  dangers  against  which  the  whole 
procedure  of  historical  investigation  and  the  theory  of 
judicial  proof  are  directed.  It  is  a  far  cry  from  the  naive 


270  THE  ESSENTIALS  OF  LOGIC 

credulity  of  the  child  to  the  methodical  skepticism  of  the 
trained  historian  and  the  legal  expert ;  yet  experience 
of  error  has  forced  this  change.  "  Our  first  natural 
attitude  toward  testimony  is  one  of  trust ;  not  because 
we  have  reasoned  that  it  is  trustworthy,  but  merely  be- 
cause we  cannot  help  it.  If  it  had  not  always  been 
natural  to  accept  the  statements  of  those  about  us  as 
substantially  true,  we  should  probably  not  be  alive  now 
to  discuss  the  matter ;  for  the  telling  of  the  truth  on  the 
one  hand  and  confidence  in  the  story  told  on  the  other 
are  very  important  means  for  the  preservation  of  the 
race."^  But  experience  soon  qualifies  this  tendency. 
We  discover  that  we  must  hear  as  much  evidence  as  we 
can,  and  then  compare,  sift,  and  weigh  it.  Such  collection, 
sifting,  and  comparing  is  at  first  rough  and  ready.  It  is 
soon  developed  into  a  careful  technique  with  accepted 
principles  and  maxims.  The  two  best  examples  of  such 
technique  are,  of  course,  historical  method  and  legal 
method.  We  shall,  in  the  main,  concern  ourselves  with 
the  principles  of  legal  method,  but  shall  now  and  then 
caU  attention  to  historical  method  and  its  manner  of 
dealing  with  the  documents  of  the  past. 

The  Modern  Critical  Attitude  toward  Testi- 
mony. "  Any  assertion,  taken  as  the  basis  of  an  in- 
ference to  the  existence  of  the  matter  asserted,  is  testi- 
mony, whether  made  in  court  or  not.  Assertions  made 
on  the  witness  stand  are  merely  the  commonest  class  of 
testimonial  evidence."  ^  Such  assertions  are,  then,  the 
raw  material  of  proof.  They  must  be  tested  until  a 
residuum  is  left  as  morally  certain  fact. 

1  Aikins,  The  Principles  of  Logic,  p.  364. 

^  Wigmore,  Principles  of  Judicial  Proof  p.  812. 


CIRCUMSTANTIAL  EVIDENCE  271 

When  a  witness's  assertion  is  examined  from  the 
logical  standpoint,  it  is  seen  to  involve  at  least  three 
elements,  perception,  memory,  and  narration.  In  the 
chapter  dealing  with  "  Observation  and  Fact,"  we  be- 
came aware  of  the  ever-present  danger  of  error  in 
both  observation  and  memory.  What  was  said  then 
could  be  reinforced  by  case  after  case  in  the  annals  of 
law.i 

"  A  thousand  mistakes  of  every  description  would  be 
avoided  if  people  did  not  base  their  conclusions  upon  prem- 
ises furnished  by  others,  take  as  established  fact  what  is 
only  possibility,  or  as  a  constantly  recurring  incident 
what  has  only  been  observed  once.  ...  I  am  assuming 
that  the  witness  is  really  desirous  of  speaking  the  truth 
and  is  merely  a  bad  observer."  ^  Much  testimony  can  be 
proved  to  be  mistaken  by  fairly  simple  tests.  "  Suppose 
a  witness  affirms  that  he  was  beaten  by  Hiov  ten  min- 
utes. Let  a  watch  be  placed  before  him  and  ask  him  to 
take  good  note  of  how  long  ten  minutes  lasts  and  then  say 
whether  it  was  really  ten  minutes.  After  a  quarter  of 
a  minute  he  will  exclaim,  *  It  certainly  did  not  last 
longer  than  that.' " 

Cross-examination  is  often  of  great  assistance  in 
determining  the  validity  of  assertions.  New  statements 
may  be  made  by  the  witness  which  will  disagree 
with  his  other  statements,  or  further  developments 
may  be  indicated.  "  In  Lincoln's  i5rst  murder  trial, 
the  chief  witness  had  testified  to  seeing  the  murder 
committed  by  the  prisoner.  In  the  cross-examination  he 
added  a  number  of  details :  that  the  shooting  was  at 

1  See  Wigmore,  Principles  of  Judicial  Proof,  pp.  296-726. 

2  Hans  Gross,  Criminal  Investigation,  p.  22. 


272  THE  ESSENTIALS  OF  LOGIC 

ten  o'clock  at  night ;  in  beech  timber ;  in  August ; 
that  he  was  twenty  feet  or  more  away ;  that  he  could 
see  the  pistol  and  how  it  hung ;  that  the  nearest  lights 
were  half  a  mile  away,  and  that  he  saw  it  all  by  moon- 
light. Lincoln  showed  that  the  moon  did  not  rise  till 
one  o'clock  in  the  morning.  Cross-examination  may 
bring  out  inconsistencies  due  to  dishonesty  as  well  as 
incompetence,  as  shown  in  this  example."  ^ 

Logic  has  little  concern  with  the  practical  difficulties 
due  to  the  temperament  of  the  witness.  There  are 
dull  and  stupid  witnesses,  timid  and  self-conscious, 
hostile,  dogged,  etc.  Logic  must,  however,  stress 
the  part  played  by  suggestion,  and  the  .difficulty 
many  people  have  of  expressing  themselves  adequately. 
The  exhaustive  study  of  testimony  in  the  modern 
schools  of  scientific  law  calls  logic,  ethics,  anthropology 
experimental  psychology,  and  psychiatry  to  its  aid. 
Race,  age,  sex,  mental  disease,  moral  character,  feeling, 
interest,  and  experience,  all  affect  the  character  of  the 
testimony  given. 

After  the  identity  of  the  witness  has  been  estab- 
lished, the  first  problem  is  :  Was  the  witness  in  a  posi- 
tion to  perceive  the  facts?  The  court  wishes  to  know 
the  witness's  opportunities.  Next  comes  the  question 
whether  he  has  any  strong  bias  or  motive  for  falsifying. 
Very  often  the  testimony  of  interested  parties  is  re- 
jected; it  is  at  least  somewhat  discounted.  When  the 
testimony  given  is  against  the  advantage  of  the  witness, 
it  is,  however,  regarded  as  having  peculiar  weight. 
Such  testimony  usually  occurs  under  cross-examina- 
tion. 

^  Quoted  from  Jones,  Logic,  Inductive  and  Deductive,  p.  272. 


CIRCUMSTANTIAL  EVIDENCE  273 

Logical  Standards  and  Tests.  There  are  certain 
logical  tests  which  are  directly  applicable  to  the  story 
told  by  a  witness.  It  must  he  self-consistent ;  it  must  he 
consistent  with  other  known  facts  of  the  case  ;  and 
must  he  consistent  with  the  larger  run  of  human  ex- 
perience. Let  us  look  at  these  three  logical  tests  some- 
what closely. 

To  be  acceptable,  the  testimony  of  a  witness  must 
be  coherent  and  self-consistent.  When  two  of  his  asser- 
tions are  shown  to  conflict,  not  only  are  we  unable  to 
decide  which  is  the  true  one,  but  we  are  also  rightly  in- 
clined to  be  suspicious  of  the  rest  of  his  story. 

Again,  if  the  story  told  conflicts  with  facts  which 
are  otherwise  known  beyond  reasonable  doubt,  doubt  is 
thereby  cast  upon  it.  This  is  especially  the  case  where 
the  facts  are  important  and  conspicuous.  The  agree- 
ment or  disagreement  of  the  particular  testimony  with 
that  advanced  by  other  witnesses  enters  here  as  con- 
tradiction or  convergent  confirmation. 

Lastly,  the  statements  made  must  not  conflict  with 
the  laws  of  nature  or  with  the  tested  possibilities  of 
the  case.  When  a  man  testifies  that  he  saw  clearly 
what  occurred  in  a  darkened  room  when  he  was  look- 
ing in  from  outside,  we  have  good  reason  to  reject  his 
testimony.  Of  course,  assertions  must  not  be  too  lightly 
and  hastily  rejected. 

These  three  tests  imply  both  internal  and  external 
evidence.  A  very  good  example  from  history  of  their 
application  is  the  determination  of  the  false  authorship 
of  the  Donation  of  Constantine.  This  famous  docu- 
ment was  the  supposed  gsant  by  the  Emperor  Constan- 
tine to  Pope  Silvester  and  his  successors,  not  only  of 


274  THE  ESSENTIALS  OF  LOGIC 

spiritual  supremacy  over  the  other  great  patriarchates 
and  over  all  matters  of  faith  and  worship,  but  also  of 
temporal  dominion  over  Rome  and  Italy  and  the  prov- 
inces, places,  and  civitates  of  the  western  regions.  A 
close  study  of  the  document,  including  the  style,  lan- 
guage, and  references,  has  convinced  scholars,  both 
Catholic  and  Protestant,  that  the  document  is  a  forgery 
dating  from  the  eighth  century.  This  painstaking  ap- 
plication of  internal  and  external  evidence  has  been 
applied  to  the  Old  and  New  Testament,  and  is  usually 
called  the  ♦  Higher  Criticism.'  It  is  very  seldom  that 
the  alleged  author  turns  out  to  be  the  real  author. 

The  Movement  of  Judicial  Proof.  Having  exam- 
ined the  nature  of  both  circumstantial  and  testimonial 
evidence,  it  may  be  well  to  glance  at  a  summary  state- 
ment of  the  actual  movement  of  evidence  and  argument. 
We  shall  refer  to  the  asserter  of  the  fact  as  the  '  Pro- 
ponent' and  the  opposer  as  the  'Opponent.'    In  the 

following  outline,  the  sign ^  signifies  '  tends  to 

prove ' ;  the  sign  o — ]>  signifies  '  tends  to  dis- 
prove ' ;  the  sign  <^  signifies  '  explains  away ' ;  letter 
T  stands  for  a  testimonial  evidential  fact ;  letter  G 
stands  for  a  circumstantial  evidential  fact. 

Circumstantial  Evidence  Process 

Probandum :  X  stabbed  Y  with  a  knife  at  a  certain  time  and 
place. 
Proponent's  Evidential  Fact  —       C= Bloody  knife  was  found  on 

X >  Probandum. 

Proponent's  Evidential  Fact  ex- 
plained by  Opponent —  C=:X  drew  it  from  the  wound 

after  the  fray  on  coming 
to  Y  's  assistance  <  Pro- 
ponent's Evidential  Fact. 


CIRCUMSTANTIAL  EVIDENCE  275 


Proponent's  Evidential  Fact  de- 
nied by  Opponent  —  C  ^  Bloody  knife  was  not  found 

on    X    — o — >  Propo- 
nent's Evidential  Fact, 
and  this  the  opponent  may  do,  either — 

(1)  by  adducing  new  evidential 

facts —  T=zM's    assertion    that    on 

searching   X    no  knife 
was  foand. 
C = No  trace  of  blood  from  the 
knife  appeared  on  X's 
garments. 

(2)  or  by  questioning  the  inference  from  the  T  or  C  on  which 
Proponent's  Evidential  Fact  itself  rested  as  a  probandum. 

Finally,  — 
Rival   New  Facts  adduced  by 

Opponent  —  C=zX  had  no  quarrel  or  other 

motive  to  stab  Y — o — > 
Probandum. 
and  T^Na  bystander  asserts  that 
X  did  not  stab  Y — o — > 
Probandum.^ 

The  MaBsing  of  Mixed  Evidence.  In  any  com- 
plex case,  a  huge  mass  of  more  or  less  conflicting  evi- 
dence is  presented  to  the  juror's  mind,  and  he  must 
arrange  it  in  such  a  way  as  to  weigh  it  correctly. 
"  Many  data,  perhaps  multifarious,  are  thrust  upon  us 
as  tending  to  produce  belief  or  disbelief.  Each  of  them 
(by  hypothesis)  has  some  probative  bearing.  Conse- 
quently, we  should  not  permit  ourselves  to  reach  a  con- 
clusion without  considering  all  of  them  and  the  relative 
value  of  each."  What  the  mind  ordinarily  does  under 
such  cases  is  to  pass  back  and  forth  from  significant 
^  Adapted  from  Wigfmore,  Principles  of  Judicial  Proof,  p.  26. 


276  THE  ESSENTIALS  OF  LOGIC 

fact  to  significant  fact  allowing  itself  to  balance  one 
fact  against  another.  The  result  is  a  drift  in  a  certain 
direction.  In  this  way,  a  series  of  subordinate  judg- 
ments is  passed,  and  these  prepare  the  field  for  more 
comprehensive  judgments  of  a  final  sort.  The  mind 
then  goes  back  over  the  material  in  the  light  of  its  ten- 
tative decision  to  see  whether  all  the  facts  fall  into  line. 
If  they  do,  the  decision  is  accepted  as  final.  The  fun- 
damental mental  necessity  is  the  ability  to  coordinate 
the  data  and  weigh  them  in  their  relation  to  one  an- 
other. Along  with  this  must  go  openness  of  mind  and 
willingness  to  go  back  and  forth  over  the  facts  with 
all  the  reasonable  hypotheses  in  mind  to  see  how  ade- 
quately they  fit. 

In  such  complex  reasoning  the  strands  of  argument 
are  so  many  and  so  interwoven  that  fallacies  of  one 
kind  or  another  are  almost  sure  to  creep  in  unless  the 
utmost  vigilance  is  exercised.  Neglect  of  other  possi- 
bilities, false  disjunction,  false  analogy,  argumentum 
ad  populum  are  fairly  common  features  of  forensic 
contests.  In  summing  up,  however,  the  fallacy  which 
should  be  most  zealously  guarded  against  is  the  fallacy 
of  the  '  neglected  aspect.'  It  is  so  easy  to  assume  that 
all  the  relevant  factors  have  been  taken  into  account 
and  have  been  given  their  due  weight ;  yet  nothing  is 
more  common  than  to  over-simplify  a  problem  and  to 
neglect  imj)ortant  causes  and  facts.  How  many  of  us 
have  committed  this  fallacy  of  neglected  aspect  in  con- 
nection with  the  European  War  or  in  connection  with 
social  problems  like  poverty  and  drunkenness ! 

The  following  newspaper  argument  against  prohibi- 
tion illustrates  this  tendency  very  well:  "You  destroy 


CIRCUMSTANTIAL  EVIDENCE  277 

the  jobs  of  people  upon  whom  about  5000  of  the  popu- 
lation depend ;  you  take  the  jobs  away  from  about 
2000  room-rent  or  house-rent  payers  or  home-owners; 
you  deprive  the  city  itself  of  about  $300,000  of  direct 
revenue,  in  the  way  of  excise  taxes  and  property  taxes ; 
you  depreciate  the  rental  value  of  about  15,000,000 
worth  of  property  in  the  town."  Granted  that  the  as- 
sertions are  correct,  "  if  the  facts  which  they  bring  for- 
ward were  the  only  ones  to  be  considered,  the  inference 
as  to  prohibition  would  be  inevitable.  If,  however,  the 
liquor  traffic  is  as  pernicious  in  its  influence  as  its  op- 
ponents claim  it  to  be,  the  benefits  which  result  from  it 
are  far  outweighed  by  the  evil  it  produces.  This  aspect 
of  the  case  is  neglected  however,  and  so  the  argument 
remains  inconclusive."  ^ 

REFERENCES 

Aikins,  The  Principles  of  Logic,  chap.  xxxv. 

Bode,  An  Outline  of  Logic,  chap.  xii. 

Hibben,  Logic,  Deductive  and  Inductive,  chap.  xiv. 

Jones,  Logic,  Inductive  and  Deductive,  pt.  in,  chap.  m. 

Wigmore,  Principles  of  Judicial  Proof,  Introductory,  asidt.  passim. 

*  Bode,  An  Outline  of  Logic,  p.  196. 


CHAPTER  XXIV 

EXPLANATION  AND  SYSTEM-FORMATION 

The  Nature  of  Explanation.  To  explain  any- 
thing is  to  show  that  it  follows  from  something  else 
already  known.  A  fact  is  explained  when  it  is  inter- 
preted by  means  of  a  law  or  a  principle.  The  specific 
is  explained  by  the  general ;  and  the  less  general  by 
the  more  general.  In  explanation,  we  move  downward 
from  niles  to  cases,  from  principles  to  their  exemplifi- 
cations. We  see  the  temporary  and  the  changing  in 
the  light  of  the  more  permanent  and  relatively  un- 
changing. 

That  all  explanation  is  in  its  essence  deduction^  has 
been  generally  recognized  by  logicians.  We  try  to  re- 
late the  given  to  those  generalizations  which  we  have 
slowly  worked  out  as  both  rules  of  action  and  rules  of 
interpretation.  We  are  not  comfortable  with  mere 
facts  which  are  unordered  and  unrelated.  They  challenge 
us  as  chaotic  and  meaningless  until  we  can  somehow 
put  them  together  as  parts  of  a  permanent  whole  which 
can  be  conceived.  Thus,  in  the  domain  of  the  physical 
sciences,  a  fact  is  felt  to  be  explained  when  it  is  re- 
lated to  the  terms  of  a  general  principle. 

The  Sentiment  of  Rationality.   A  given  fact  by 

itself  seems  like  a  shot  out  of  a  pistol.    It   is,  —  our 

senses  are,  perhaps,  witnesses  to  its  occurrence,  —  hut 

it  stands  in  isolation.    So  far  as  this  is  the  case,  our 

^  Sigwart,  Logic,  vol.  ii,  p.  417. 


EXPLANATION  AND  SYSTEM-FORMATION    279 

minds  cannot  really  grasp  it  and  give  it  meaning  for  the 
simple  reason  that  past  experience  cannot  be  brought  to 
bear  upon  it.  It  remains,  then,  a  brute  sensational  event 
to  which  our  concepts  cannot  attach  themselves.  But 
because  our  minds  try  to  find  some  point  of  attachment, 
some  way  of  striking  up  a  friendship  with  the  event, 
they  feel  baffled  and  uncomfortable.  Thus,  the  senti- 
ment of  rationality,  the  desire  to  explain  and  interpret, 
is  an  expression  of  the  very  mode  of  working  of  human 
consciousness.  When  any  event  or  thing  is  given,  our 
minds  seek  to  find  relations  between  it  and  other  facts 
already  familiar  and  more  or  less  interpreted.  In  this 
way  it  is  assimilated  and  given  a  local  habitation  and  a 
name.  "  All  knowledge,  all  science,  thus  aims  to  grasp 
the  meaning  of  objects  and  events,  and  this  process 
always  consists  in  taking  them  out  of  their  apparent 
brute  isolation  as  events,  and  finding  them  to  be  parts 
of  some  larger  whole,  suggested  hy  therriy  which,  in 
turn,  accounts  for^  explains^  interprets  them;  i.e., 
renders  them  significant.  Suppose  that  a  stone  with 
peculiar  markings  has  been  found.  What  do  these 
scratches  mean  ?  So  far  as  the  object  forces  the  rais- 
ing of  this  question,  it  is  not  understood  ;  while  so  far 
as  the  color  and  form  that  we  see  mean  to  us  a  stone, 
the  object  is  understood.  It  is  such  peculiar  combina- 
tions of  the  understood  and  the  non-understood  that 
provoke  thought.  If  at  the  end  of  the  inquiry,  the 
markings  are  decided  to  mean  glacial  scratches,  obscure 
and  perplexing  traits  have  been  translated  into  mean- 
ings already  understood :  namely,  the  moving  and 
grinding  power  of  large  bodies  of  ice  and  the  friction 
thus  induced  of  one   rock  upon  another.    Something 


280  THE  ESSENTIALS  OF  LOGIC 

already  understood  in  one  situation  has  been  transferred 
and  applied  to  what  is  strange  and  perplexing  in  an- 
other, and  thereby  the  latter  has  become  plain  and 
familiar,  i.e.,  understood.  This  summary  illustration 
discloses  that  our  power  to  think  effectively  depends 
upon  possession  of  a  capital  fund  of  meanings  which 
may  he  applied  when  desired. ^^  ^ 

The  Rdle  of  Concepts.  Concepts  play  a  tremen- 
dously important  part  in  both  reasoning  and  explana- 
tion. Let  us  try  to  bring  out  the  deductive  side  of 
explanation  referred  to  above  by  stressing  the  role  of 
concepts  in  experience.  Because  concepts  are  accepted 
organizations  of  experience,  anything  related  to  them  is 
naturalized,  so  to  speak,  and  becomes,  thenceforth,  a 
citizen  of  the  mind.  Relation  to  the  concepts  gives  it 
its  credentials.  Thus  the  foundation  of  all  explanation 
is  the  capacity  of  the  mind  to  generalize  and  to  secure 
by  means  of  analysis,  abstraction  and  synthetic  imagin- 
ation those  general  ideas  and  principles  which  illumin- 
ate and  organize  experience.  Our  study  of  induction 
has  been  essentially  a  tracing  of  the  steps  and  activities 
involved  in  the  attainment  of  such  concepts.  We  have 
seen  how  facts  are  observed  and  selected  at  the  instance 
of  some  problem,  how  comparisons  and  analyses  are 
made,  how  guesses  at  the  causes  or  principles  at  work 
are  made  by  fertile  minds,  how  these  guesses  are  tested 
and  modified  and  re-tested,  how  systems  of  conceptual 
knowledge  slowly  arise  and  are  used  to  give  meaning 
to  new  facts  as  well  as  to  the  old  from  which  they 
sprung.  Now  it  is  to  this  property  of  such  conceptual 
systems  to  give  meaning  to  new  facts  that  we  are  call- 
»  Dewey,  How  We  Think,  pp.  117-18. 


EXPLANATION  AND  SYSTEM-FORMATION    281 

ing  attention.    It  is  in  this  property  that  explanation 
consists. 

It  is  significant  that  this  explanatory  property  of 
concepts  can  be  connected  with  the  syllogism.  It  will 
be  remembered  that  the  typical  syllogism  has  a  univer- 
sal proposition  for  its  major  premise.  The  minor  pre- 
mise then  states  a  concrete  case  which  can  be  subsumed 
under  the  universal  principle,  while  the  conclusion  con- 
sists of  the  actual  identification  of  the  concrete  case 
with  the  principle. 

All  cases  of  M  are  cases  of  P/ 
iS  is  a  case  of  M ; 
Therefore  5  is  a  case  of  P. 

Both  JWand  P  are  abstract  characters  or  universals; 
they  are  concepts  which  have  gradually  been  achieved 
by  the  human  mind  as  the  result  of  that  sentiment  of 
rationality  to  which  we  have  referred  above.  "  This  is, 
in  fact,  a  world  in  which  general  laws  obtain,  in  which 
universal  propositions  are  true,  and  in  which  reasoning 
is  therefore  possible."  We  reason  down  from  such 
general  concepts  to  facts  and  thereby  explain  them. 

Concepts  are  "  instruments  (1)  of  identification ; 
(2)  of  supplementation ;  and  (3)  of  placing  in  a  sys- 
tem. Suppose  a  little  speck  of  light  hitherto  unseen  is 
detected  in  the  heavens.  Unless  there  is  a  store  of 
meanings  to  fall  back  upon  as  tools  of  inquiry  and 
reasoning,  that  speck  of  light  will  remain  just  what  it 
is  to  the  senses  —  a  mere  speck  of  light.  For  all  that 
it  leads  to,  it  might  as  well  be  a  mere  irritation  of  the 
optic  nerve.  Given  the  stock  of  meanings  acquired  in 
prior  experience,  this  speck  of  light  is  mentally  attached 
hy  means  of  appropriate  concepts.    Does  it  indicate 


282  THE  ESSENTIALS  OF  LOGIC 

asteroid,  or  comet,  or  a  new-forming  sun,  or  a  nebula 
resulting  from  some  cosmic  collision  or  disintegration? 
Each  of  these  conceptions  has  its  own  specific  and  dif- 
ferentiating characters,  which  are  then  sought  for  by 
minute  and  persistent  inquiry.  As  a  result,  then,  the 
speck  is  identified,  we  wiU  say,  as  a  comet.  Through  a 
standard  meaning,  it  gets  identity  and  stability  of 
character.  Supplementation  then  takes  place.  All  the 
known  qualities  of  comets  are  read  into  this  particular 
thing,  even  though  they  have  not  been  as  yet  observed. 
All  that  astronomers  of  the  past  have  learned  about 
the  paths  and  structure  of  comets  becomes  available 
capital  with  which  to  interpret  the  speck  of  light. 
Finally,  this  comet-meaning  is  itself  not  isolated ;  it  is 
a  related  portion  of  the  whole  system  of  astronomic 
knowledge.  Suns,  planets,  satellites,  nebulae,  comets, 
meteors,  star-dust  —  all  these  conceptions  have  a  cer- 
tain mutuality  of  reference  and  interaction^  and  when 
the  speck  of  light  is  identified  as  meaning  a  comet,  it 
is  at  once  adopted  as  a  full  member  in  this  vast  king- 
dom of  beliefs."^  A  fact  which  is  identified,  supple- 
mented in  this  broad  way,  and  put  into  a  system  is 
explained ;  it  has  been  removed  from  its  isolation, 
given  relations  to  other  things,  and  interpreted  by 
general  principles. 

Proof  and  Explanation.  A  proposition  is  proved 
when  it  is  shown  to  follow  from  accepted  premises, 
while  a  fact  or  specific  rule  is  explained  when  it  is 
shown  to  be  the  natural  consequence  of  principles.  It 
is  evident  that  proof  and  explanation  are  essentially  the 
same ;  in  both  the  deductive  element  dominates.  Thus 
1  Dewey,  How  We  Think,  pp.  126-27. 


/    EXPLANATION  AND  SYSTEM-FORMATION    283 

far  we  have  looked  at  the  problem  mainly  from  the 
angle  of  explanation ;  let  us  now  examine  it  from  the 
side  of  proof.  Why  does  the  application  of  the  major 
premise  to  a  case  constitute  proof  ?  "  The  answer  is 
that  it  serves  to  connect  the  conclusion  with  the  system 
of  concepts  or  general  principles  that  have  previously 
been  accepted.  When  one  sees  that  the  new  suggestion 
comes  under  the  old  principles,  the  belief  that  has  been 
developed  for  the  system  of  knowledge  extends  to  the 
particular  instance.  The  laws  and  principles  that  have 
been  established  and  accepted  are  connected  with  the 
conclusion  that  is  in  doubt,  and  the  doubt  disappears. 
Each  doubt  that  is  solved  increases  the  belief  in  the 
principle,  since  it  assures  its  connection  with  a  new 
fact.  It  should  be  added  that  the  process  of  reference 
to  the  system  of  knowledge,  not  merely  justifies  the  old, 
but  also  increases  the  number  of  applications  of  the 
old.  It  extends  its  application,  and  when  the  conclu- 
sion itseK  is  confirmed  in  practice,  the  general  principle 
receives  new  warrant."  ^  This  quotation  brings  out  ad- 
mirably the  fact  that  knowledge  consists  of  the  growth 
of  systems  of  knowledge  which  must  take  up  new  facts 
into  themselves.  Such  systems  possess  mental  author- 
ity, and  proof  is  the  repression  of  this  authority. 
Combined  with  such  authority  there  must  exist  the 
mental  perception  of  the  inner  coherence  of  system  and 
fact.  The  system  must  be  capable  of  assimilating  the 
fact;  it  is  here  that  the  deductive  element  enters. 

Systems  are  tentative.  Systems  are  no  longer  re- 
garded as  having  either  their  final  form  or  content. 
There  is  less  dogmatism  in  all  fields  to-day  than  formerly. 

1  Pillsbury,  Essentials  of  Psychology,  pp.  234-35. 


284  THE  ESSENTIALS  OF  LOGIC 

The  trial-and-error  feature  of  knowledge  is  more  clearly 
recognized.  We  may  allow  ourselves  to  speak  of  sys- 
tems of  knowledge  as  growths,  but  we  must  not  be  mis- 
led by  the  organic  analogy.  There  are  differences  as 
well  as  similarities  between  the  growth  of  systems  of 
ideas  and  the  growth  of  organisms.  The  difference  I 
would  stress  lies  in  this,  that  the  innate  or  determined 
factor  is  less  obviously  in  control  in  systems  of  knowl- 
edge than  in  the  growth  of  a  particular  organism.  To 
put  this  point  concretely,  systems  of  knowledge  do  not 
have  an  heredity.  If  we  desire  an  analogy,  it  is  far 
better  to  compare  the  development  of  knowledge  in  a 
particular  field  with  the  adaptation  of  a  human  being 
to  his  environment.  Habits  are  necessarily  tentative  and 
revocable  just  as  ideas  are.  Man  has  found  that  he 
must  relinquish  habits  and  customs  and  institutions, 
much  as  he  is  forced  at  times  to  give  up  ideas  once 
fondly  cherished.  In  both  domains,  however,  we  have 
good  reason  to  believe  that  it  is  not  a  case  of  mere 
supplanting,  but  that  there  is  a  genuine  advance,  a 
real  progress.  I  cannot  do  better  in  this  connection 
than  to  quote  what  Bertrand  Russell  writes  in  regard 
to  the  attitude  and  contributions  of  Henri  Poincare  to 
modern  science  :  "  Another  reason  which  makes  a  phi- 
losophy of  science  specially  useful  at  the  present  time 
is  the  revolutionary  progress,  the  sweeping-away  of 
what  had  seemed  fixed  landmarks,  which  has  so  far 
characterized  this  century,  especially  in  physics.  The 
conception  of  the  '  working  hypothesis,'  provisional, 
approximate,  and  merely  useful,  has  more  and  more 
pushed  aside  the  comfortable  eighteenth-century  con- 
ception of  '  laws  of  nature.'  Even  the  Newtonian  dy- 


EXPLANATION  AND  SYSTEM-FORMATION    285 

namics,  which  for  over  two  hundred  years  had  seemed 
to  embody  a  definite  conquest,  must  now  be  regarded 
as  doubtful,  and  as  probably  only  a  first  rough  sketch 
of  the  ways  of  matter.  And  thus,  in  virtue  of  the  very 
rapidity  of  our  progress,  a  new  theory  of  knowledge  has 
to  be  sought,  more  tentative  and  more  modest  than  that 
of  more  confident  but  less  successful  generations."  ^ 

Levels  of  Explanation.  We  may  distinguish  dif- 
ferent levels  in  explanations.  The  first  stage  is  classifi- 
cation. The  dominant  purpose  at  this  level  is  to  gather 
objects,  compare  them,  and,  finally,  classify  them.  When 
systems  of  classification  are  worked  out,  specimens  can 
be  ordered  in  relation  to  one  another  and  new  cases 
can  be  identified  and  put  in  their  proper  place.  No 
matter  how  external  and  superficial  such  systems  of 
classification  are,  they  represent  the  beginning  of  sci- 
entific explanation ;  things  are  removed  from  their  iso- 
lation. As  the  system  of  classification  is  penetrated  by 
perception  of  more  essential  characteristics,  this  stage 
passes  to  the  next,  which  may  be  called  ♦  the  empirical.' 

At  the  empirical  level,  subordinate  laws  and  princi- 
ples are  discovered.  For  example,  many  strands  of  cau- 
sal uniformity  and  laws  of  action  and  reaction  become 
known.  In  medicine,  it  is  discovered  that  certain  drugs 
have  definite  effects  upon  the  organism,  and  that  the 
individual  reacts  in  certain  ways  to  various  toxins.  In 
chemistry,  laws  and  principles  are  often  known  while 
there  is  doubt  of  their  real  significance.  One  of  the 
best  historical  instances  of  the  empirical  stage  is  the 
situation  in  astronomy  after  Kepler  and  before  New- 
ton. Kepler  discovered  that  the  planetary  orbits  are 
1  Russell,  Preface  to  Poincar^'s  Science  and  Method,  pp.  6-7. 


286  THE  ESSENTIALS  OF  LOGIC 

elliptical  instead  of  circular  as  had  been  supposed. 
Kepler  generalized  the  known  facts  in  terms  of  his 
three  laws  :  (1)  that  the  planets  move  in  ellipses  round 
the  sun,  with  the  sun  in  one  of  the  foci ;  (2)  that  they 
describe  equal  areas  in  equal  times ;  (3)  that  the  cubes 
pf  their  mean  distances  vary  as  the  squares  of  their 
periodic  times.  Although  many  suggestions  were  made 
and  analysis  of  motion  was  carried  further  by  various 
physicists,  it  remained  to  Newton  to  carry  astronomy 
over  to  the  third  level,  that  of  explanation  proper. 

Newton  did  two  things :  "  He  conceived  that  the 
force  which  deflected  the  planets  into  their  orbits  was 
the  same  as  that  which  made  bodies  fall  to  the  earth; 
or,  to  put  it  differently,  he  identified  celestial  attraction 
with  terrestrial  gravity,  and  conceived  the  earth  as  es- 
sentially yaZ^iw^  out  of  a  straight  path  towards  the  sun, 
and  the  moon  towards  the  earth ;  and  he  invented  a 
mathematical  calculus  by  which  he  could  work  out 
what  were  the  theoretical  consequences  of  the  princi- 
ples he  assumedy  ^  Examining  these  two  things  which 
Newton  accomplished,  we  see  that  they  were,  first,  an 
extension  of  the  idea  of  gravity  to  all  cases  of  physical 
bodies,  an  act  of  universalization,  and  second,  the  en- 
trance of  a  distinctly  deductive  element.  The  more  de- 
duction increases^  the  more  has  the  level  of  explanation 
been  achieved. 

The  ideal  often  held  by  the  physical  sciences  is  well 
expressed  by  Helmholtz.  In  his  little  book  on  the  Coji- 
servation  of  J^orce,  he  writes :  "  So  that  at  last  the  task 
of  Physics  resolves  itself  into  this,  to  refer  phenomena 
to  inalterable  attractive  and  repulsive  forces  whose  in- 
1  Joseph,  An  Introduction  to  Logic,  p.  479. 


EXPLANATION  AND  SYSTEM-FORMATION    287 

tensity  varies  with  distance.  The  solution  of  this  task 
would  at  the  same  time  be  the  condition  of  Nature's 
complete  intelligibility."  For  Helmholtz,  in  other  words, 
partial  explanations  in  science  must  be  subsumed  under 
completer,  more  deductive  ones  until  the  ideal  he  sets 
forth  is  reached.  This  is  not  the  place  to  discuss  this 
ideal  from  the  philosophical  side.  It  may  be  of  interest 
to  the  student,  however,  to  point  out  that  it  is  a  clear 
statement  of  the  mechanical  view  of  the  world. 

General  Explanation  and  Specific  Explanation* 
Sometimes  the  scientist  is  primarily  interested  in  dis- 
covering general  laws  and  then  carrying  these  laws 
themselves  back  to  still  more  general  principles ;  at 
other  times,  he  wishes  to  explain  particular  facts.  The 
more  concrete  the  science,  the  more  is  there  an  interest 
in  the  particular  for  its  own  sake.  Thus,  history  is 
mainly  concerned  with  events  or  customs  which  have 
been  brought  about  by  the  interaction  of  many  forces 
and  agencies.  Suck  events  cannot  he  deduced  from,  ele- 
mentary  and  universal  principles.  There  is  not  repeti- 
tion enough,  and  the  factors  concerned  are  too  complex 
and  mutable.  Where  deduction  can  afford  genuine 
prediction,  there  must  be  relative  simplicity.  It  is  pos- 
sible to  predict  the  transit  of  Venus,  the  effect  of  Ice- 
land spar  upon  a  beam  of  light,  and  the  product  of  the 
union  of  hydrogen  and  oxygen ;  but  it  is  impossible  to 
predict  what  will  happen  after  the  present  great  war. 
The  historian  must  grope  his  way  to  generalizations 
which  are  only  tendencies ;  his  chief  interest  must  be 
directed  to  the  understanding  of  events  which  have  al- 
ready happened  by  tracing  their  known  antecedents. 
But  when  the  physical  scientist  seeks  to  understand  just 


288  THE  ESSENTIALS  OF  LOGIC 

why  some  specific  event  happened,  he,  also,  must  search 
out  all  the  relevant  circumstances.  The  main  difference 
is  that  time  is  a  less  important  factor  for  him  than  it  is  for 
the  historian.  In  fact,  as  we  pass  from  the  abstract  sci- 
ences through  the  biological  to  the  human  sciences,  time 
increases  in  importance.  Institutions  and  events  are 
best  interpreted  when  we  know  how  they  arose.  Our 
conclusion  is,  that  sciences  differ  in  their  emphases. 
Some,  the  more  abstract,  aim  to  furnish  general  prin- 
ciples only  and  leave  the  specific  and  the  unique  to  the 
concreter  sciences ;  while  the  more  concrete  sciences  de- 
vote much  of  their  attention  to  particular  events  which 
are  judged  to  be  important. 

Typical  Systems  of  Knowledge.  Many  logicians 
have  attempted  to  classify  the  sciences  according  to 
fiome  one  principle.  Such  classifications  must,  however, 
be  recognized  to  be  relative  to  the  principle  adopted. 
Suppose  that  we  use  the  relative  proportion  of  general 
law  and  specific  fact  as  the  standard  of  division.  We 
shall  then  commence  with  mathematics,  pass  to  me- 
chanics, thence  to  chemistry ;  from  chemistry  we  shall 
go  to  biology  and  psychology,  and,  finally,  to  the 
human  sciences  which  all  involve  the  methods  of  his- 
tory. Corresponding  to  such  a  passage  from  the  more 
abstract  to  the  more  concrete  is  a  change  in  the  nature 
of  the  material  studied.  We  begin  with  the  abstract 
properties  of  physical  things  and  end  with  highly  or- 
ganized and  changing  wholes.  Let  us  glance  briefly  at 
the  two  extremes  to  see  what  the  respective  systems  are 
like  and  how  they  are  developed. 

Mathematics  is  a  typical  deductive  science.  It  does 
not  involve  an  appeal  to  particular  facts  which  must  be 


EXPLANATION  AND  SYSTEM-FORMATION    289 

generalized.  Geometry,  for  example,  does  not  begin  with 
concrete  things  as  do  the  physical  sciences,  but  with 
certain  concepts,  given  in  definitions,  axioms,  and  pos- 
tulates, and  with  the  nature  of  abstract  space.  "  It  is 
because  space  relations  are  unaffected  by  locality  that 
what  I  have  seen  to  be  a  property  of  this  circle  must 
be  a  property  of  any  circle."  ^  What  mathematics  rests 
on,  then,  is  an  apprehension  of  the  relations  between 
the  elements  of  space  and  quantity.  In  a  very  real  sense, 
there  are  no  particular  instances  which  have  relevant 
qualities  of  their  own.  Thus^  the  data  of  mathematics 
are  few  in  number  and  essentially  changeless^  which  is 
another  way  of  saying  that  they  are  conceptual  rather 
than  perceptual.  The  generalization-aspect  of  the  sci- 
ence is  taken  care  of  at  the  very  start.  It  follows  that 
the  test  of  the  truth  of  any  conclusion  cannot  be  of  a 
perceptual  character;  rather  is  it  of  the  nature  of  a 
recognized  agreement  with  the  principles  and  theorems 
already  developed.  A  geometrical  system  is  primarily  a 
realm  of  internal  consistency.  "  Thus  the  space-intui- 
tion which  is  so  essential  an  aid  to  the  study  of  logic 
is  logically  irrelevant :  it  does  not  enter  into  the  prem- 
ises when  they  are  properly  stated,  nor  into  any  step 
of  the  reasoning."  ^  The  true  method  of  studying  geom- 
etry is  to  conceive  "  interesting  simple  figures,  such 
as  the  triangle,  the  parallelogram,  and  the  circle,  and 
to  investigate  the  correlations  between  their  various 
parts.  The  geometer  has  in  his  mind  not  a  detached 
proposition,  but  a  figure  with  its  various  parts  mutually 

^  Joseph,  An  Introduction  to  Logic,  p.  506.  Mr.  Joseph's  chapter  on 
"  Mathematical  Reasoning  "  is  well  worth  study. 
*  Whitehead,  Introduction  to  Mathematics,  p.  242. 


290  THE  ESSENTIALS  OF  LOGIC 

inter-dependent."  ^  Such  figures  are  seen  in  the  light 
of  the  primary  set  of  axioms  and  postulates.  We  may 
say,  then,  that  mathematics  deals  with  abstract  entities 
which  are  conceived. 

The  historical  sciences,  on  the  other  hand,  are  founded 
on  concrete  data.  These  data  may  be  classified  into  two 
groups,  material  facts  and  testimony.  The  first  duty 
of  the  historian  is  to  gather  all  the  data  available.  As 
a  rule,  such  data  consist  of  documents,  which  are  records 
in  various  forms  of  the  thoughts  and  actions  of  men  of 
former  times.^  No  one  who  has  not  given  some  thought 
to  the  matter  can  appreciate  the  effort  required  to 
bring  about  even  a  partially  satisfactory  fund  of  mate- 
rial, especially  where  the  very  distant  past  is  concerned. 
The  next  step  is  the  estimation  of  the  relative  value 
of  the  various  items.  It  is  to  this  problem  that  much 
of  the  historian's  ingenuity  is  directed.  Both  internal 
and  external  evidence  must  be  adduced,  analyses  made, 
and  exact  scholarship  brought  to  bear.  As  material  is 
evaluated,  a  certain  body  of  more  or  less  certain  fact  is 
established  and  worked  up  into  an  interpretative  narra- 
tive of  the  development  of  a  people.  Such  a  narrative 
is  being  constantly  purified  by  the  elimination  of  data, 
too  credulously  accepted,  and  deepened  by  the  addition 
of  new  data  and  new  points  of  view. 

The  logician's  interest  in  history  concerns  the  meth- 
ods used  to  secure  the  material,  the  presence  of  selec- 
tion, analysis  and  interpretation,  the  part  played  by 
guiding-ideas,  and  the  importance  of  constructive  im- 
agination.   Modern  scientific  method  in  history  is  a 

*  Whitehead,  Introduction  to  Mathematics,  p.  238. 

*  See  Lauglois  and  Seignobos,  Introduction  to  the  Study  of  History. 


EXPLANATION  AND  SYSTEM-FORMATION    291 

monument  to  the  ideal  of  truth  in  a  complex  field  in 
which  difficulties  exist  at  every  step.  The  historian  has 
been  forced  by  his  problems  into  self -consciousness  so 
that  there  are  several  excellent  discussions  of  historical 
method  easily  obtainable.  Let  us  look  at  some  of  the 
conclusions  which  bear  upon  the  elements  of  induction. 

First  of  all,  there  have  been  spirited  controversies  in 
regard  to  the  purpose  of  history.  There  have  been  po- 
litical historians,  moral  historians,  sociological  histori- 
ans ;  and,  corresponding  to  these,  there  have  been  his- 
torical schools.  Upon  only  one  point  have  all  agreed, 
viz.,  that  truth  must  be  the  ideal.  Within  minor  diver- 
gencies, a  large  guiding-idea  is  now  held  in  common. 
Development  is  the  keynote.  "  We  have  noted  that  the 
scope  of  history  has  broadened  by  taking  more  and 
more  factors  into  account.  Wars  and  statecraft  are  now 
regarded  as  a  less  important  part  of  national  life.  This 
has  come  about  not  merely  through  curiosity  to  find 
out  how  people  lived  in  time  past,  but  in  the  search 
after  the  explanation  of  national  development.  .  .  . 
The  thread  upon  which  the  story  of  any  nation  hangs 
is  development  from  the  past  into  the  present."  ^  His- 
tory seeks  to  explain,  just  as  any  other  developed  sci- 
ence does,  but  it  explains  by  development.  The  com- 
position of  causes  back  of  an  event  or  institution  is 
always  more  or  less  unique. 

The  search  for  documents  is  a  science  in  itself  and 
involves  the  collaboration  of  many  subordinate  sci- 
ences, such  as  palaeography,  epigraphy,  and  philology. 
But  this  technique  is  controlled  by  the  plans  and  ideas 
of  investigators.  Given  the  material,  the  next  step 
1  Vincent,  Historical  Research,  p.  10. 


292  THE  ESSENTIALS  OF  LOGIC 

is  the  determination  of  facts.  "The  document  is  the 
starting-point,  the  fact  the  goal.  Between  this  start- 
ing-point and  this  goal  he  has  to  pass  through  a  com- 
plicated series  of  inferences,  closely  interwoven  with 
each  other,  in  which  there  are  innumerable  chances  of 
error;  while  the  least  error,  whether  committed  at  the 
beginning,  middle,  or  end  of  the  work,  may  vitiate  all 
his  conclusions."  ^  The  facts  of  history,  in  other  words, 
are  judgments,  not  observations. 

There  are  many  sources  of  error  of  a  distinctly  men- 
tal character.  Sometimes  there  is  reason  to  doubt  the 
good  faith  of  the  author.  Sympathy  often  plays  its  se- 
lective and  distorting  part ;  again,  vanity  and  deference 
to  public  opinion  may  be  at  work.  The  result  of  expe- 
rience has  been  the  rise  of  a  defensive  canon,  called 
'  methodical  distrust.'  This  canon  wiU  bring  home  to 
the  student  the  discussion  of  some  of  the  causes  of  error 
in  observation  given  in  Chapter  XVII.  With  a  char- 
acteristic statement  of  it  we  shall  close  the  present  dis- 
cussion of  scientific  systems,  for  it  generalizes  that  atti- 
tude of  reflection  and  criticism  which  it  is  the  task  of 
logic  on  its  practical  side  to  enforce.  "  We  must  not 
postpone  doubt  till  it  is  forced  upon  us  by  conflicting 
statements  in  documents  ;  we  must  begin  by  doubting."  ^ 
We  must  try  to  secure  "that  methodically  analytical, 
distrustfid,  not  too  respectful  turn  of  mind  which  is 
often  mystically  called  '  the  critical  sense '  but  which  is 
nothing  else  than  an  unconscious  habit  of  criticism."  ^ 

1  Lanpflois  and  Seignobos,  Introduction  to  the  Study  of  History,  p.  64. 

2  Bid.,  p.  157.  »  Ibid.,  p.  190. 


EXPLANATION  AND  SYSTEM-FORMATION    293 

REFERENCES 

Dewey,  How  We  Think,  chap.  ix. 

Jones,  Logic,  Inductive  and  Deductive,  pt.  ill,  chaps.  I  and  m. 

Joseph,  An  Introduction  to  Logic,  chap.  xxni. 

Pillsbury,  Essentials  of  Psychology,  chap.  ix. 

Poincar^,  Science  and  Method,  passim. 

Whitehead,  Introduction  to  Mathematics,  chap.  xvi. 

Langlois  and  Seignobos,  Introduction  to  the  Study  of  History. 


CHAPTER  XXV 

TRUTH  AND  ITS  TESTS 

Back  to  the  Definition  of  Logic.  Logic  was  de- 
fined as  '  the  science  of  the  principles  and  conditions  of 
correct  thinking.'  This  definition  was  offered  as  a  guide- 
post  to  direct  attention  to  the  general  character  of  the 
subject.  Now  that  we  have  covered  the  various  topics, 
we  must  come  back  to  the  definition,  analyze  the  terms, 
and  permit  ourselves  to  suggest  and  briefly  discuss  some 
of  the  larger  and  more  philosophical  problems  which 
have  all  along  hovered  in  the  background.  What  stu- 
dent has  not  asked  himself  Pilate's  question.  If  logic 
deals  with  the  conditions  and  principles  of  correct  think- 
ing, it  must  contain  some  standard  of  correctness.  While 
it  is  not  the  business  of  logic  to  decide  what  ideas  are 
true,  —  i.e.,  what  the  empirical  content  of  truth  is,  — 
it  does  seem  to  be  a  part  of  its  task  to  give  analytic 
knowledge  of  the  meaning  of  truth  and  of  the  princi- 
ples and  methods  actually  used  in  testing  assertions 
which  lay  claim  to  this  apotheosis. 

In  order  to  think  correctly,  we  must  think  both  con- 
sistently and  truly.  Let  us  look  at  these  two  pre- 
requisites for  a  moment.  It  is  impossible  to  think  truly 
without  thinking  consistently,  but  it  is  possible  to  think 
consistently  without  thinking  truly.  But  very  few  men 
want  to  think  only  consistently.  The  one  is  a  means  to 
the  other,  valued  largely  because  of  this  relation. 

The  Nature  of  Consistent  Thinking.  To  think 


TRUTH  AND  ITS  TESTS  295 

consistently  means  to  avoid  self-contradiction.  The 
conclusions  we  draw  must  be  related  to  the  premises  we 
accept  in  accordance  with  logical  necessity.  Consistent 
thinking  must  not  sin  against  the  Laws  of  Thought  and 
must  contain  a  recognized  harmony  among  its  parts. 
When  such  thinking  is  also  in  agreement  with  the  facts, 
we  are  apt  to  speak  of  it  as  true  and  its  product  as  truth 
or  valid  knowledge. 

We  have  come  to  see  that  clear  and  well-organized 
ideas  are  essential  conditions  of  consistent  thinking. 
Definition  and  analysis  help  to  make  the  ideas  we  use 
clear  and  unambiguous,  while  classification,  in  which 
concepts  are  ordered  in  relations  of  coordination,  sub- 
ordination, and  superordination,  is  another  prime  con- 
dition of  good  thinking.  Only  knowledge  which  is  dis- 
tinct and  well  organized  can  be  handled  without  serious 
danger  of  error. 

Thought  discovers  internal  relations  between  proposi- 
tions of  such  a  character  that  one  Jbllows  from  others. 
The  sign  of  such  a  logical  relation  is  words  like  '  there- 
fore '  and  '  hence.'  Mis  I^  and  S  is  M;  therefore  S  is 
I^.  If  we  grant  the  premises,  it  is  impossible  to  deny 
the  conclusion  without  self-contradiction.  If  the  damp- 
ness of  the  sidewalk  is  the  sign  of  either  rain  or  dew, 
this  case  of  dampness  signifies  that  it  rained  last  night 
or  that  there  was  a  fall  of  dew.  The  mind  feels  itself 
forced  to  draw  the  conclusion,  once  it  has  admitted  a 
general  rule  and  recognized  a  specific  instance  as  com- 
ing under  the  rule.  Such  logical  necessity  is,  in  a  sense, 
the  inverse  of  the  act  of  generalization.  Were  we  un- 
able to  generalize,  we  should  be  unable  to  infer,  and  the 
word,  therefore,  would  have  no  meaning  for  us.  This 


296  THE  ESSENTIALS  OF  LOGIC 

fact  reveals  the  intimate  relation  of  induction  and  de- 
duction. 

The  Lavrs  of  Thought.  We  have  postponed  the 
treatment  of  the  traditional  Laws  or  Axioms  of  Thought, 
because  they  are  apt  to  appear  trivial  and  meaningless 
when  taken  up  at  the  beginning  without  a  logical  context. 
These  primary  axioms  of  thought  are  three  in  number 
and  state  the  recognized  conditions  of  consistent  think- 
ing. So  far  as  I  can  see,  they  arise  from  and  express 
the  very  nature  of  conceptual  thinking.  For  that  rea- 
son, however,  they  are  as  self-evident  as  the  axioms  of 
Euclidian  geometry.  After  formulating  them,  I  shall 
try  to  relate  them  to  the  act  of  thinking. 

The  Laws  of  Thought  are :  — 

(1)  The  Law  of  Identity.  A  is  A. 

(2)  The  Law  of  Contradiction.  A  is  not  not-^. 

(3)  The  Law  of  Excluded  Middle.  Everything  ia 
either  A  or  not-^. 

It  is  obvious  that  these  axioms  need  some  interpreta- 
tion in  order  to  give  meaning  to  the  symbolic  form  in 
which  they  are  stated.  We  shall  start  with  the  Law  of 
Identity,  develop  its  meaning,  and  then  show  that  the 
other  laws  are  simply  further  explications  of  it  in  the 
light  of  the  negative. 

The  Law  of  Identity  carries  us  back  to  the  nature  of 
concepts.  A  concept  is  a  mental  object  which  we  can 
hold  before  the  attention,  think  about,  and  distinguish 
from  other  objects.  But  before  this  can  be  done,  these 
mental  objects  must  have  a  certain  degree  of  stability 
and  distinctness  of  content.  Hazy,  vague,  uncertain 
thoughts  are  condemned  by  logic  because  they  are  not 
full-fledged  ideas.  We  all  know  when  we  have  such  im- 


TRUTH  AND  ITS  TESTS  297 

mature  concepts  before  our  minds  —  at  least,  we  do 
when  we  are  reflective  and  have  learned  to  distinguish 
between  concepts  and  words.  Since  one  of  the  princi- 
ples of  logic  is  non-ambiguity,  one  of  its  ideals  must  be 
clear  and  distinct  concepts.  Now^  such  clear  and  dis- 
tinct concepts  are  recognizable  and  distinguishable  J^rom 
others.  It  is  this  fact  that  the  Law  of  Identity  points 
out.  No  thought  and  no  judgment  is  possible  where 
concepts  cannot  be  held  before  the  mind,  retained,  re- 
produced, and  recognized  as  the  same.  This  sense  of 
sameness  is,  as  James  phrased  it,  "  the  very  keel  and 
backbone  of  thinking." 

The  Law  of  Contradiction  is  the  negative  side  of  the 
Law  of  Identity.  If  we  are  able  to  present  clear  ideas 
to  the  mind,  we  must  also  be  able  to  distinguish  them 
from  one  another.  To  apprehend  A  is  also  to  know  that 
it  is  not  not-^. 

There  is  another  form  of  the  Law  of  Contradiction 
which  concerns  itself  with  judgment  rather  than  with 
the  character  of  concepts.  This  other  form  is  usually 
called  the  Aristotelian  and  is  as  follows  :  "  It  is  impos- 
sible that  the  same  predicate  can  both  belong,  and  not  be- 
long, to  the  same  subject,  at  the  same  time,  and  in  the 
same  sense."  This  formulation  brings  out  sharply  the  na- 
ture and  meaning  of  contradiction  by  calling  attention 
to  the  fact  that  the  human  mind  cannot  accept  the  judg- 
ments '  A  is  B,^  and  '  A  is  not.  B '  at  the  same  time. 

The  Law  of  Excluded  Middle  is  a  further  definition 
of  the  relation  between  a  term  and  its  contradictory. 
It  asserts  that  of  two  contradictory  assertions  one  is 
necessarily  true.  There  can  be  no  third  possibility.  In 
formal  logic,  this  principle  appears  in  the  fact  that 


«0S  THE  ESSENTIALS  OF  LOGIC 

there  are  only  two  qualities,  the  affirmative  and  the 
negative. 

The  Postulates  of  Logic.  Besides  these  axioms, 
certain  postulates  are  sometimes  advanced  as  essential 
to  logic.  The  following  is  a  partial  list :  (1)  Every  as- 
sertion is  either  true  or  false.  (2)  Some  proposition 
may  be  recognized  as  true.  (3)  The  mind  is  able  to 
apprehend  objects.  (4)  There  are  universal  connections 
in  nature,  and  some  at  least  of  these  can  be  discovered. 

(5)  The  world  is  essentially  the  same  for  all  observers. 

(6)  Individuals  who  communicate  can  mean  essentially 
the  same  by  their  terms.  The  investigation  of  these 
postulates  is  usually  assigned  to  epistemology  and 
metaphysics. 

The  Question  of  Truth.  Consistency  with  other 
propositions  is  not  by  itself  a  sufficient  criterion  of 
truth.  An  assertion  may  foUow  with  due  logical  neces- 
sity from  temporarily  accepted  premises,  but  such  an 
internal  relation  cannot  guarantee  the  system  as  a  whole. 
While  the  accepted  premises  justify  the  conclusion, 
they  themselves  must  be  justified.  But  does  not  this 
situation  lead  us  into  a  difficulty  ?  Can  we  have  any- 
thing more  than  consistency?  Suppose  that  we  use  the 
term  '  valid '  for  a  conclusion  which  follows  from  ac- 
cepted premises  with  logical  necessity.  The  question 
which  confronts  us  is  this,  Can  we  attain  anything  but 
valid  assertions  ?  But,  if  this  be  the  case,  our  ultimate 
premises  must  either  be  given  with  their  credentials  by 
some  sort  of  extra-logical  intuition,  or  must  be  accepted 
on  authority,  or,  finally,  be  postulated.  Is  there  any 
way  to  avoid  this  unwelcome  series  of  disjunctions? 

I  hope  that  the  student  has  seen  that  this  way  of 


TRUTH  AND  ITS  TESTS  299 

approach  to  the  question  of  truth  has  stressed  the  de- 
ductive side  of  logic  to  the  exclusion  of  induction. 
Were  thinking  only  deductive,  we  should  be  compelled 
to  face  the  unwelcome  alternatives  outlined  above.  It 
has  been  the  prime  fallacy  of  many  of  the  philosophical 
systems  of  the  past  to  seek  some  one  principle  from 
which  to  deduce  reality  as  experienced.  In  my  opinion, 
such  an  attempt  is  illogical  because  it  exalts  deduction 
over  induction  and  does  not  see  that  knowledge  is  a 
growth  in  which  both  aspects,  or  phases,  of  thinking  are 
at  work. 

*  Validity '  is,  then,  essentially  a  deductive  term 
while  '  truth '  corresponds  more  to  that  intimate  inter- 
play of  induction  and  deduction  which  has  been  pre- 
sented in  our  study  of  science.  It  will  be  remembered 
that  there  are  three  elements,  or  distinguishable  mental 
processes  in  all  systematic  investigation,  namely,  the 
inductive  element  par  excellence^  whose  principle  is  ob- 
servation with  its  fidelity  to  fact ;  the  generalizing  and 
hypothesis-forming  element ;  and,  lastly,  deductive  rea- 
soning out  of  implications.  These  elements  are  inter- 
twined according  to  the  exigencies  of  the  case.  It  is 
out  of  the  inductive-deductive  interaction  of  fact  and 
theory  that  truth,  as  distinct  from  mere  validity,  arises. 

The  Criteria  of  Truth.  It  has  been  customary  to 
speak  of  truth  and  to  contrast  it  with  error.  This  col- 
lective way  of  speaking  about  truth  as  a  body  of  doc- 
trine has  too  often  led  people  to  think  of  truth  in  a 
mystical  fashion.  Even  critical  thinkers  have  com- 
mitted the  '  fallacy  of  abstract  terms,'  ^  and  thought  of 
truth  as  an  abstract  entity.  In  order  to  avoid  this  dan- 

^  See  chapter  in. 


300  THE  ESSENTIALS  OF  LOGIC 

ger,  it  is  best  to  distinguish  between  true  ideas  and 
false  ideas.  And,  by  ideas,  we  shall  mean  assertions, 
propositions,  judgments,  theories,  in  fact  all  mental 
objects  in  regard  to  which  we  make  the  truth-claim. 
Our  present  purpose  is  to  discover  the  actual,  empirical 
tests  which  are  used  in  investigation  to  decide  between 
ideas  which  tentatively  claim  truth  and  yet  conflict. 
WTiat  are  the  criteria  of  true  ideas  ?  And  what  is  the 
logical  setting  of  these  criteria  f 

Reviewing  our  study  of  systematic  investigation,  we 
note  that  investigation  is  begun  only  when  some  prob- 
lem arises.  Every  such  problem  must  have  a  concrete 
and  specific  character.  In  truth,  the  scientist  is  well 
aware  that  his  first  task  is  to  define  his  problem,  for  any 
lack  of  clearness  in  the  statement  of  the  problem  is  cer- 
tain to  thwart  his  efforts.  To  work  on  an  iU-defined 
problem  is  like  hunting  for  something  of  which  one 
has  no  clear  picture.  The  next  step  is  the  separation  of 
what  is  certain  from  what  is  uncertain.  He  wants  to 
know  what  he  can  depend  on,  what  is  beyond  question 
for  the  purpose  in  hand.  The  logician  calls  the  certain- 
ties of  the  field  relevant  to  the  specific  problem  the 
'  data,'  and  contrasts  the  conjectures  and  hypotheses, 
which  arise  in  the  fertile  mind  of  the  scientist,  with 
these  data  as  *  theory.'  It  must  be  remembered  that 
such  theories  develop  in  the  mind  of  the  expert  who 
has  detailed  familiarity  with  what  has  been  discovered 
and  achieved  in  this  particular  field  and  in  those  ad- 
joining. An  hypothesis  is  not  external  to  the  knowledge 
of  the  field  but  is  a  genuine  branch  of  it.  The  tree  of 
human  knowledge  is  vigorous  and  puts  forth  many 
shoots,  some  of  which  must  be  lopped  off.  The  process 


TRUTH  AND  ITS  TESTS  301 

of  selecting  among  competing  explanations  by  marking 
their  capacity  to  cover  and  organize  the  facts  and  so 
solve  the  specific  problem  is  called  verification.  Veri- 
fication involves  responsibility  to  fact,  freedom  from 
self-contradiction,  and  a  flexible  harmony  with  other 
accepted  theories  which  have  passed  through  the  same 
test.  In  any  particular  case,  such  testing  is  a  complex 
process  in  which  the  mind  works  back  and  forth  be- 
tween data  and  theory,  adding  new  data  and  modifying 
the  theory.  The  criteria  of  truth  are  not  external  but 
internal.  It  is  absurd  to  look  for  some  touchstone  which 
can  be  applied  in  a  mechanical  fashion  to  propositions 
claiming  truth. 

Degrees  of  Belief.  Assertions  are  not  made  with 
the  same  degree  of  assurance,  nor,  to  state  the  same  fact 
in  more  psychological  language,  is  there  only  one  degree 
of  belief.  The  traditional  logic  was  accustomed  to  rec- 
ognize this  fact  in  its  theory  of  modals.  '  The  earth  re- 
volves around  the  sun'  is  an  assertoric  judgment.  A 
dictum  is  asserted  flatly.  *  It  may  rain  this  afternoon  * 
is  a  problematic  judgment.  In  science,  the  stage  of 
conjecture  represents  the  problematic  mode.  '  Gravita- 
tion may  be  explained  in  terms  of  electricity,'  '  Mass 
may  turn  out  to  be  a  dynamic  effect  of  something  more 
ultimate,'  are  examples.  An  apodeictic  judgment,  on  the 
other  hand,  expresses  a  sense  of  logical  necessity.  The 
gi'ounds  for  the  judgment  are  given  or  intimated. 
*  There  must  be  a  presidential  election  this  year '  is  apo- 
deictic. The  ground  intimated  is,  of  course,  the  federal 
law  on  the  subject. 

Modality  reflects  the  fact  that  ideas  have  different 
settings.  Beliefs  are  held  with  more  or  less  faith.  The 


802  THE  ESSENTIALS  OF  LOGIC 

upper  limit  of  belief  is  dogmatic  certainty,  while  the 
other  extreme  is  a  low  degree  of  probability.  The  logi- 
cian encourages  individuals  to  give  up  dogmatic  cer- 
tainty and  to  make  practical  certainty  the  highest  de- 
gree of  belief.  There  is  a  continuous  shading  of  belief 
from  mere  probability,  in  which  the  evidence  is  weak, 
to  practical  certainty  in  which  there  is  no  longer  any 
factually  motivated  doubt.  Rational  belief  is  belief 
founded  on  grounds,  and  such  grounds  must  ultimately 
come  back  to  critically  tested  fact. 

What  the  Attainment  of  True  Ideas  implies. 
There  are  at  least  four  things  implied  in  the  attain- 
ment of  true  ideas :  (1)  the  ability  to  obtain  facts  (ob- 
servations, testimony,  evidence)  ;  (2)  the  right  to 
make  use  of  past  experience  which  is  not  challenged  by 
reasonable  doubt;  (3)  the  Principle  of  Universal  Con- 
nections, the  Uniformity  of  Nature,  the  Law  of  Uni- 
versal Causation  ;  (4)  the  mental  capacity  for  analysis, 
conjecture,  construction,  and  deductive  reasoning. 

These  four  things  are  largely  self-explanatory  when 
taken  in  the  light  of  what  has  already  been  said  about 
them  in  the  preceding  chapters.  Unless  we  could  obtain 
facts,  which  are  assertions  about  which  there  is  no 
motivated  doubt,  it  would  be  impossible  to  generalize, 
to  form  hypotheses,  or  to  verify  by  the  convergence  of 
evidence.  Unless  past  knowledge  were  applicable,  it 
would  be  impossible  to  have  guidance  in  an  attack  on 
new  problems  or  to  determine  what  was  relevant  and 
what  irrelevant ;  again,  it  would  be  impossible  to  build 
up  systems  of  knowledge  such  as  are  found  in  the  vari- 
ous sciences  as  well  as  in  practical  life.  Knowledge  is, 
as  we  have  so  often  pointed  out,  a  growth.  While  the 


TRUTH  AND  ITS  TESTS  303 

old  may  be  modified  by  the  new  facts  and  theories,  it 
yet  remains  as  something  substantial  within  which  to 
work.  That  universal  connections  exist  and  can  be  dis- 
covered is  a  postulate  which  underlies  all  scientific  in- 
vestigation. It  cannot  be  proved  in  any  demonstrative 
way,  but  is  suggested  and  in  a  way  verified  by  expe- 
rience. Finally,  logic  assumes  that  the  mental  capaci- 
ties which  human  beings  possess,  working  upon  the  ma- 
terial given  by  observation  and  testimony,  are  able  to 
achieve  ideas  which  give  genuine  knowledge.  To  doubt 
this  ability  to  attain  knowledge  is  for  logic  an  ultimate 
scepticism  which  it  refuses  to  acknowledge.  Both  our 
practical  and  our  intellectual  instincts  revolt  against  the 
suggestion  that  what  we  take  to  be  knowledge  is  not 
knowledge. 

The  Meaning  of  Truth.  Having  given  the  empiri- 
cal criteria  of  '  truth '  and  their  logical  setting,  let  us 
be  bold  enough  to  discuss  the  meaning  of  this  term. 
What  do  we  mean  by  '  true '  ideas  ?  How  do  such 
ideas  differ  from  '  false '  ideas  ?  Controversial  battles 
have  been  waged  in  philosophy  over  the  meaning  of 
these  terms.  Into  the  details  of  such  controversies,  it 
is  not  here  the  place  to  enter.  We  must  be  brief  and 
clear,  and  trust  that  the  position  adopted  will  commend 
itself  to  the  reason  of  those  who  have  carefully  studied 
the  preceding  pages. 

Let  us  admit  the  hazard  that  what  we  take  to  be 
true  may  not  be  true.  The  problem  still  remains  that 
we  mean  something  by  this  term.  An  idea  is  true  which 
meets  the  empirical  criteria  and  which  we  therefore 
take  to  be  a  case  of  knowledge.  An  idea  is  true  which 
has  stood  the  test  of  motivated  doubt,  has  come  out 


804  THE  ESSENTIALS  OF  LOGIC 

victorious,  and,  due  to  that  fact,  is  accepted  by  the 
mind  as  fulfilling  its  claim  to  be  an  idea  of,  or  about, 
something.  It  is  the  very  nature  of  an  idea  to  claim  to 
give  knowledge.  When  this  claim  is  granted  by  the 
mind,  the  idea  is  accredited  or  accepted  as  genuine 
knowledge ;  and  the  term  true  is  used  to  express  this 
attitude  of  approval.  Thus,  it  is  a  contrast  term  with 
'  false '  as  its  counterpart.  Just  as  actions  are  quali- 
fied as  right  or  wrong,  so  ideas  —  i.e.,  judgments,  pro- 
positions, assertions  —  are  qualified  as  true  or  false. 
This  latter  qualification  gets  its  meaning,  however,  from 
the  claim  to  be  cases  of  knowledge  which  it  is  the  very 
nature  of  such  judgments  to  assert. 

There  can  be  little  doubt  that  the  methods  by  which 
ideas  are  tested  enter  into  the  meaning  of  truth  to  a 
greater  or  lesser  extent.  What  is  called  'pragmatism' 
is  a  stimulating  but,  I  believe,  one-sided  emphasis  on  this 
aspect  9f  the  meaning  of  truth.  "  True  ideas,^^  writes 
James,  "  are  those  that  we  can  assimilate,  validate, 
corroborate  and  verify.  liaise  ideas  are  those  that  we 
cannot.  That  is  the  practical  difference  it  makes  to  us 
to  have  true  ideas ;  that,  therefore,  is  the  meaning  of 
truth,  for  it  is  all  that  truth  is  known-as."  ^  It  will  be 
noticed  that  the  meaning  of  being  an  actual  case  of 
knowledge,  which  is  a  part  of  the  content  and  setting  of 
every  assertion,  is  omitted.  This  aspect  is,  in  our  opin- 
ion, fundamental.  The  logician  who  understands  his 
science  does  not  deny  the  empirical  character  of  the 
criteria  of  trueness,  but  he  does  assert  that  the  claim 
of  an  idea  to  be  knowledge  is  also  essential.  "  Knowl- 
edge is  an  achievement  and  possession  of  minds  as  these 
1  James,  Pragmatism,  p.  201. 


TRUTH  AND  ITS  TESTS  305 

have  evolved  under  the  stimulus  of  their  environment. 
As  a  meaning,  knowledge  precedes  truth,  which  is  a 
reflective  deepening  of  the  sense  of  knowledge  in  the 
light  of  an  awakened  doubt.  The  criteria  of  truth  are, 
therefore,  the  same  as  those  of  knowledge.  Thus  truth 
is  accepted  and  tested  knowledge.  To  say  that  an  idea 
is  true  is  to  say  that  it  is  actually  a  case  of  knowledge 
as  it  claims  to  be.  Truth  is  knowledge  triumphant  in- 
stead of  knowledge  militant ;  yet  it  is  knowledge,  as 
can  be  seen  when  we  combine  the  two  terms  and  speak 
of  true  knowledge."  ^ 

Truth  and  the  Will  to  believe.  Of  recent  years 
there  have  been  several  stimulating  essays  on  the  rela- 
tion of  will  and  our  passional  nature  in  general  to  be- 
lief. By  consensus  of  opinion,  the  two  most  striking  of 
these  are  James's  The  Will  to  Believe  and  Clifford's 
The  Ethics  of  Belief  .  These  two  writers  hold  positions 
which  are  different  both  in  their  tenor  and  in  their  con- 
clusions. It  will  repay  us  to  examine  their  discussions 
of  the  foundations  of  belief  for  this  will  introduce 'us 
to  the  larger  setting  of  logic. 

Let  us  begin  with  The  Will  to  Believe.  As  a  psy- 
chologist, James  rightly  first  considers  the  actual  psy- 
chology of  human  opinion.  "  When  we  look  at  certain 
facts,  it  seems  as  if  our  passional  and  volitional  nature 
lay  at  the  root  of  all  our  convictions.  When  we  look 
at  others,  it  seems  as  if  they  could  do  nothing  when  the 
intellect  had  once  said  its  say."  ^  Taking  up  the  latter 
facts  first,  he  writes :  "  Does  it  not  seem  preposterous 

1  Sell  are,  Critical  Realism,  p.  282. 

2  James,  The  Will  to  Believe;  page  references  are  to  Representative 
Essays  in  Modern  Thought. 


306  THE  ESSENTIALS  OF  LOGIC 

on  the  very  face  of  it  to  talk  of  our  opinions  being 
modifiable  at  will?  Can  we,  by  just  willing  it,  believe 
that  Abraham  Lincoln's  existence  is  a  myth,  and  that 
the  portraits  of  him  in  Mc  Chive's  Magazine  are  all  of 
some  one  else?  .  .  .  We  can  say  any  of  these  things, 
but  we  are  absolutely  impotent  to  believe  them ;  and 
of  just  such  things  is  the  whole  fabric  of  the  truths 
that  we  do  believe  in  made  up,  —  matters  of  fact,  im- 
mediate or  remote,  as  Hume  said,  and  relations  between 
ideas,  which  are  either  there  or  not  there  for  us  if  we 
see  them  so,  and  which  if  not  there  cannot  he  put  there 
hy  any  action  of  our  own^*  (p.  76).  I  feel  that  it  is 
best  to  quote  this  side  of  James's  teaching  quite  fully, 
since  justice  has  not  been  done  to  it.  James  permits 
the  '  will  to  believe '  only  in  certain  fields  and  under 
certain  circumstances.  "  The  talk  of  believing  by  our 
volition  seems,  then,  from  one  point  of  view,  simply 
silly.  From  another  point  of  view  it  is  worse  than  silly ; 
it  is  vile.  When  one  turns  to  the  magnificent  edifice  of 
the  physical  sciences,  and  sees  how  it  was  reared ;  what 
thousands  of  disinterested  moral  lives  of  men  lie  buried 
in  its  mere  foundations ;  what  patience  and  postpone- 
ment, what  choking  down  of  preference,  what  submis- 
sion to  the  icy  laws  of  outer  fact  are  wrought  into  its 
very  stones  and  mortar ;  how  absolutely  impersonal  it 
stands  in  its  vast  augustness,  —  then  how  besotted 
and  contemptible  seems  every  little  sentimentalist  who 
comes  blowing  his  voluntary  smoke  wreaths,  and  pre- 
tending to  decide  things  from  out  of  his  private  dream  " 
(p.  78). 

But,  as  James  points  out,  there  is  an  interaction  be- 
tween our  knowledge,  our  values,  our  aspirations,  and 


TRUTH  AND  ITS  TESTS  307 

our  prejudices.  The  mind  is  an  organic  whole,  and  it 
is  impossible  to  find  an  intellect  separate  from  the 
movement  of  experience.  Facts  and  theories  are  not 
independent,  for  their  discovery,  selection,  relative  im- 
portance and  control,  of  the  outlook  of  the  individual ; 
and  this  outlook  is  a  synthesis  of  ideas  and  feelings. 
That  this  is  the  case  we  have  tried  to  bring  out  in  the 
study  of  induction.  But  the  logician  urges  the  individ- 
ual to  allow  the  outlook  to  be  more  a  function  of  in- 
vestigation, to  make  the  factual  side  the  control-side. 
The  logician  sets  an  ideal  which  he  admits  is  seldom 
approached.  This  control  of  outlook  by  'fact'  is  the 
aim  which  lies  back  of  the  inductive  principle  of  fidelity 
to  fact  and  the  internal  criteria  of  truth,  the  conver- 
gence of  relevant  evidence.  Thus  logic  stresses  the 
avoidance  of  error,  on  the  one  hand,  and  the  positive 
methods  of  attaining  new  truth  on  the  other.  Its  aim 
is  to  make  the  individual  critically  reflective  toward 
assertions  and  beliefs. 

Let  us  now  turn  to  the  thesis  which  James  defends : 
"  Our  passional  nature  not  only  lawfully  may^  hut 
must^  decide  an  option  between  propositions^  whenever 
it  is  a  genuine  option  that  cannot  by  its  nature  be  de- 
cided on  intellectual  grounds  ;  for  to  say^  under  such 
circumstances,  '  Do  not  decide,  but  leave  the  question 
open^  is  itself  a  passional  decision, — just  like  decid' 
ing  yes  or  no  —  and  is  attended  with  the  same  risk  of 
losing  the  truth."  What  strikes  the  logician  in  this 
thesis  is  the  assumption  that  there  are  problems  "  which 
by  their  very  nature  cannot  be  decided  on  intellectual 
grounds  "  (p.  81).  It  is  this  assumption  that  the  logician 
cannot  admit  if  by  intellectual  grounds  are  meant  factual 


808  THE  ESSENTIALS  OF  LOGIC 

grounds.  Such  problems  could  not  be  formulated  and 
defined. 

But  James  at  least  suggests  that  other  problems  than 
non-rational  ones  are  also  to  be  treated  by  our  passional 
nature.  And  here  there  is  an  ambiguity  in  his  treat- 
ment. As  against  Clifford,  he  insists  that  we  do  not 
need  to  shut  our  eyes  to  a  possibility  of  belief  just  be- 
cause the  problem  has  not  been  settled  and  there  is  also 
a  possibility  of  error.  With  this  I  agree.  There  are 
degrees  of  belief ;  and,  when  evidence  can  be  advanced 
both  for  and  against  a  position,  neither  affirmation  nor 
negation  should  be  dogmatic.  I  can  understand  why 
such  a  temperament  as  James's  rebelled  against  the  stoi- 
cism of  Clough,  Huxley,  and  Clifford  which  sang:  — 

It  fortifies  my  soul  to  know 
That,  though  I  perish,  Truth  is  so. 

When  there  is  probability  only,  probability  is  by  ita 
very  nature  both  for  and  against.  The  probability  of 
throwing  a  six-spot  is  one  sixth  and  the  chances  against 
are  five  sixths.  James  has  the  right  to  stress  the  prob- 
ability for,  while  Clifford  has  an  equal  right  to  stress 
the  negative  side,  the  motivated  doubt. 

But  there  runs  through  James  the  suggestion  of  an- 
other test  of  truth  than  that  worked  out  by  science  and 
logic.  It  is  not  prominent,  but  it  is  present  enough  to 
have  led  many  to  interpret  his  position  in  accordance 
with  it.  This  second  standard  consists  in  an  appeal  to 
personal  feelings  and  satisfactions  as  a  foundation 
for  truth.  Such  feelings  are  facts,  but  they  are  not 
the  only  facts,  nor  are  they  the  least  changing  and  com- 
mon of  facts.  To  make  them  the  dominant  criteria  is, 
therefore,  to  forsake  an  objective  and  thorough  inves- 


TRUTH  AND  ITS  TESTS  309 

tigation  in  favor  of  what  experience  has  proved  to  be 
personal  and  incomplete. 

The  Logic  of  Doubt.  In  contrast  to  the  essay  by 
James,  Clifford's  treatment  savors  almost  of  a  justifica- 
tion of  doubt.  And,  from  the  logician's  standpoint, 
much  can  be  said  in  favor  of  such  an  attitude.  Belief, 
as  a  rule,  takes  care  of  itself,  while  doubt  and  open- 
mindedness  are  trained  habits  not  easily  acquired.  Clif- 
ford stresses  what  may  be  called  the  '  ethical  aspect ' 
of  logic ;  and  in  his  attitude  there  is  much  that  reminds 
us  of  the  Puritan  and  the  Stoic.  James  was  a  brilliant, 
tender-minded,  broad-minded  mystic;  Clifford  was  a 
rigorous,  tough-minded,  intellectual  idealist. 

'•  A  shipowner  was  about  to  send  to  sea  an  emigrant 
ship.  He  knew  that  she  was  old,  and  not  overwell 
built  at  the  first ;  that  she  had  seen  many  seas  and 
climes,  and  often  had  needed  repairs.  Doubts  had  been 
suggested  to  him  that  possibly  she  was  not  seaworthy. 
These  doubts  preyed  upon  his  mind,  and  made  him  un- 
happy ;  he  thought  that  perhaps  he  ought  to  have  her 
thoroughly  overhauled  and  refitted,  even  though  this 
should  put  him  to  great  expense.  Before  the  ship 
sailed,  however,  he  had  succeeded  in  overcoming  these 
melancholy  reflections.  .  .  .  He  would  dismiss  from 
his  mind  all  ungenerous  suspicions  about  the  honesty 
of  builders  and  contractors.  In  such  ways  he  acquired 
a  sincere  and  comfortable  conviction  that  his  vessel 
was  thoroughly  safe  and  seaworthy  .  .  .  ;  and  he  got 
his  insurance  money  when  she  went  down  in  midocean 
and  told  no  tales. 

"  What  shall  we  say  of  him  ?  Surely  this,  that  he 
was  verily  guilty  of  the  death  of  those  men.    It  is  ad- 


810  THE  ESSENTIALS  OF  LOGIC 

mitted  that  he  did  sincerely  believe  in  the  soundness  of 
his  ship;  but  the  sincerity  of  his  conviction  can  in  no 
wise  help  him,  because  he  had  no  right  to  believe  on 
such  evidence  as  was  before  hhn.  He  had  acquired  his 
belief  not  by  honestly  earning  it  in  patient  investiga- 
tion, but  by  stifling  his  doubts."  ^ 

Clifford's  conclusion  is :  "  It  is  wrong  always,  every- 
where, and  for  any  one,  to  believe  anything  upon  insuf- 
ficient evidence  "  (p.  64).  "  '  But,'  says  one,  *  I  am  a 
busy  man ;  I  have  no  time  for  the  long  course  of  study 
which  would  be  necessary  to  make  me  in  any  degree  a 
competent  judge  of  certain  questions,  or  even  able  to 
understand  the  nature  of  the  arguments.'  Then  he 
should  have  no  time  to  believe"  (p.  64).  It  must  have 
been  this  last  pronouncement  which  made  James  caU 
him  " that  delicious  enfant  terrible"  Let  us  soften  it 
somewhat  by  saying  that  he  should  have  no  time  for 
dogmatic  belief,  for  that  belief  which  shuts  out  evi- 
dence when  it  comes  and  passes  harshly  and  uncom- 
promisingly into  action. 

REFERENCES 

Bode,  An  Outline  of  Logic,  chap.  XV. 

James,  The  Will  to  Believe  and  other  Essays  in  Popular  Philos- 
ophy. 
James,  Pragmatism,  chap.  vi. 
Clifford,  The  Ethics  of  Belief  . 
Gibson,  The  Problem  of  Logic,  chaps,  i  and  m. 
Sellars,  Critical  Realism,  chap.  x. 

1  Clifford,  The  Ethics  of  Belief  ,  Representative  Essays,  pp.  46-47. 


QUESTIONS  AND  EXERCISES 

CHAPTER  I 

1.  Analyze  the  definition  of  logic  given,  and  compare  it 
with  definitions  to  be  found  in  other  texts. 

2.  Distinguish  between  a  theoretical  and  an  applied  sci- 
ence. Give  examples  of  both. 

3.  What  is  meant  by  'utilitarian'  when  the  term  is  used  in 
its  narrower  sense? 

4.  Point  out  and  explain  why  logic  has  a  practical  value  in 
education. 

5.  Name  the  various  kinds  of  logic.  Why  have  these 
developed? 

6.  With  what  other  sciences  is  logic  related? 

7.  How  does  the  purpose  of  logic  differ  from  that  of  rhetoric? 

8.  To  what  extent  do  logic  and  psychology  have  the  same 
subject-matter  ? 

9.  Where  does  logic  find  its  material?  Why  is  introspec- 
tion alone  not  sufficient? 

10.  Recall  an  actual  case  of  reasoning  and  try  to  analyze  it. 

CHAPTER  II 

1.  State  some  of  the  mental  processes  to  which  the  term 
'thinking'  is  applied.  Give  examples  to  bring  out  dif- 
ferent levels  of  thinking. 

2.  Distinguish  between  'imagination,'  'memory,'  and  'rea- 
soning.'  Make  two  illustrations  of  each. 

3.  Whataresomeof  the  social  conditions  of  thought?  Name 
some  of  the  great  periods  in  history  distinguished  by 
mental  boldness  and  energy. 

4.  Can  you  name  any  great  men  who  pwed  much  to  some 
stimulus  which  awakened  their  mental  curiosity? 

5.  "Thinking  arises  out  of  the  need  for  adjustment." 
Explain. 

6.  What  processes  are  preliminary  to  reasoning?  Distin- 
guish between  'perception'  and  'conception.' 


812  QUESTIONS  AND  EXERCISES 

7.  Collect  five  statements  which  you  would  call  'facts.' 
Can  you  find  any  element  of  inference  or  theory  in  them? 

8.  Take  any  field  in  which  you  are  especially  interested, 
and  show  that  your  insight  has  increased  with  further 
study. 

9.  Give  at  least  four  cases  where  your  perception  of  a  thing 
or  of  an  event  has  been  changed  by  further  knowledge. 

10.  Do  you  think  that  the  public  schools  in  America  stimu- 
late genuine  thinking  as  much  as  is  desirable?  Be  pre- 
pared to  support  your  opinion. 

CHAPTER  III 

1.  Distinguish  between  a  'logical  term*  and  a  'word.* 

2.  In  the  following  list,  point  out  which  terms  are  concrete 
and  which  are  abstract:  — 

virtue  education  solitude     life 

American  democracy  asparagus  time  will 

detachment  consciousness     auto  cavalry 

iron  man  paper        fate 

3.  Make  a  list  of  five  examples  of  collective  terms. 

4.  Distinguish  between  general  and  singular  terms.  Make 
a  list  of  five  of  each  kind. 

5.  Do  you  think  that  the  distinction  between  singular  and 
general  can  be  applied  to  abstract  terms? 

6.  Explain  the  fallacy  of  hypostatization.  Give  three 
examples  which  show  at  least  an  approach  to  this 
fallacy. 

7.  What  are  relative  terms?  Give  five  examples. 

8.  Explain  the  danger  in  discussions  about  'poverty,* 
'educational  progress,'  'the  growth  of  democracy.* 

9.  Distinguish  between  positive  and  negative  terms.  Give 
three  examples  of  each.  Is  the  form  always  an  index  to 
the  meaning? 

10.  Explain  the  distinction  between  'denotation*  and  'con- 
notation.' 

11.  Make  a  series  of  at  least  six  terms  arranged  in  order  of 
increasing  denotation.  Arrange  the  same  terms  in  order 
of  increasing  connotation. 

12.  Show  that  terms  which  do  not  have  any  connotation 
still  have  meaning. 


QUESTIONS  AND  EXERCISES  313 

CHAPTER  IV 

1.  Why  is  language  such  an  important  condition  of  think- 
ing? 

2.  State  the  logical  law  of  language. 

3.  What  are  some  of  the  causes  of  ambiguity? 

4.  Give  ten  examples  of  univocal  words.  Are  technical 
terms  always  univocal? 

5.  In  the  following  exercises  select  those  terms  of  which 
the  meaning  is  most  uncertain.  State  and  justify  the 
meaning  which  you  think  belongs  to  the  term  in  its 
present  context:  — 

(1)  We  should  live  according  to  Nature. 

(2)  All  men  have  natural  rights. 

(3)  America  is  a  democratic  country. 

(4)  International  law  must  be  binding  on  all  peoples. 

6.  Make  a  list  of  five  words  which  have  decidedly  changed 
their  meaning  during  the  last  hundred  years. 

7.  Distinguish  between  vagueness  and  ambiguity.  Show 
why  abstract  terms  are  peculiarly  liable  to  vagueness. 

8.  Try  to  formulate  the  divergent  notions  of  '  force,'  *  mat- 
ter,' and  *  motion '  that  are  expressed  or  implied  in  the 
following  extracts  from  Buechner's  Force  and  Matter:  — 

"No  force  without  matter  —  no  matter  without 
force.  One  is  no  more  possible,  and  no  more  imagin- 
able by  itself  than  the  other,  .  .  .  Force  and  matter 
are  fundamentally  the  same  thing,  contemplated 
from  diflferent  standpoints.  In  the  material  world 
we  know  of  no  example  of  a  particle  of  matter  not 
endowed  with  force  or  working  by  it.  We  must  further 
admit  on  closer  investigation,  that  matter  as  such 
could  make  no  impression  on  our  sense-organs  or 
minds;  it  can  only  do  this  by  means  of  the  forces 
united  with  or  at  work  within  it.  A  piece  of  lead  held 
in  the  hand  presses  on  it  because  of  the  attractive 
force  of  the  earth  and  so  produces  the  idea  of  weight. 
.  .  .  Nothing  can  prove  to  us  the  real  existence  of  a 
force,  except  the  properties,  changes  and  movements, 
which  we  become  conscious  of  in  matter,  and  these 
we  call  different  'forces'  according  to  the  resemblances 
or  differences  in  such  manifestations;  any  knowledge 


814  QUESTIONS  AND  EXERCISES 

of  them  by  other  ways  is  impossible.  .  .  .  Force  may 
be  defined  as  a  condition  of  activity  or  a  motion  of 
matter  or  of  the  minutest  particles  of  matter  or  a 
capacity  thereof;  yet  more  precisely,  as  an  expression 
for  the  reason  of  a  possible  or  actual  movement.  .  .  . 

"Motion  must  be  regarded  as  an  eternal  and  insepa- 
rable projierty  or  as  a  necessary  condition  of  matter. 
Matter  without  motion  exists  no  more  than  matter 
without  force;  motion  without  matter  exists  as  little 
as  force  without  matter.  Nor  can  motion  be  deduced 
from  any  force,  for  it  is  the  very  essence  of  force  it- 
self, and  can  therefore  have  no  origin,  but  must  be  in 
all  places.  .  .  .  The  most  solid  body  owes  its  condi- 
tion only  to  the  mutual  attractive  force  of  its  minutest 
particles,  which  continually  oscillate  or  swing  round 
the  so-called  center  of  gravity,  and  without  which  it 
would  at  once  fall  to  pieces.  That  these  particles  are 
never  able  to  attain  a  condition  of  relative  rest  is 
proved  by  the  universally  present  force  of  heat,  which 
is  known  to  be  nothing  more  than  a  mode  of  motion 
and  which,  since  all  bodies  without  exception  contain 
heat,  keep  these  smallest  particles  or  molecules  in  a 
state  of  continual  movement.  .  .  .  Motion  must  there- 
fore be  regarded  as  the  primal  condition  or  in  some 
measure  as  the  soul  of  matter."  * 

CHAPTER  V 

1.  What  is  classification?  Ghxt  ®f  what  need  does  it  arise? 

2.  Distinguish  between  'artificial'  and  'natural'  classi- 
fications. 

3.  How  has  the  theory  of    evolution  affected    scientific 
classification? 

4.  What  is  a  'dichotomous'  division?    Under  what  condi- 
tions might  it  be  advantageous? 

5.  Criticize  the  following  divisions:  — 

(1)  Religions,    into    Christian,    Mohammedan,    and 
non-Christian. 

(2)  Pictures,  into  paintings,  engravings,  posters,  and 
pen-and-ink  sketches. 

>  Quoted  from  Bode,  An  Outline  of  Logic. 


QUESTIONS  AND  EXERCISES  316 

(3)  Schools,  into  technical,  vocational,  and  public. 

(4)  Furniture,  into  Colonial,  Sheraton,  Adams,  oflSce, 
and  home. 

(5)  PoUtical  parties,  into  Republican,  Radical,  and 
Conservative. 

6.  Divide  and  subdivide  the  following:  — 
Governments,  Sciences,  Sports,  Schools. 

7.  State  and  explain  the  technical  terms  used  in  division. 

8.  What  part  does  purpose  play  in  both  classification  and 
division? 

CHAPTER  VI  ' 

Why  is  definition  needed? 
2.  Show  the  relation  between  'definition*  and  'classifica- 
tion.' 
7       is.  Define  the  following  terms  by  proximate  genus  and  es-7  J^***"^ 
Kj-I     sen tial  difference: —  V    JP'^^^ 

*  ]  Democracy,  Education,  Tariff,  Politics,  American,    <J    ^ 

Honor,  Wealth,  Neutrality. 
Examine  the  following  definitions  to  see  whether  they 
conform  to  the  logical  rules  of  definition:  —  -  .      , 

(1)  The  body  is  the  emblem  or  visible  garment  of  the  / ') 
soul.  ^  .         ^^ 

(2)  Life  is  a  continuous  adjustment  of  internal  to  ex-  t.\W** 
ternal  relations. 

(3)  A  phonograph  is  a  mechanism  for  recording  and  !#.*'•  jjV*^ 
reproducing  sounds.  'Gl»«-»<?'^ 

(4)  Life  is  the  opposite  of  death.    t*V***  ***^, 

(5)  Psychology  is  the  science  of  the  processes  whereby  [ir«^* 
an  individual  becomes  aware  of  a  world  of  objects  yj"*  V>^ 
and  adjusts  his  actions  accordingly.^ 

(6)  Psychology  is  the  science  of  the  phenomena  of  \j^o  ~*^ 
consciousness.^ 

(7)  Education  is  the  eternal  process  of  superior  ad-  ^ 
justment  of  the  physically  and  mentally  developed,  '»»*;^ft>>' 
free,  conscious  human  being    to   God,  as  mani-    *v*-<^^ 
fested  in  the  intellectual,  emotional,  and  volitional      "^ 
environment  of  man.'  V- 

(8)  Education  is  conscious  or  voluntary  evolution.*  y^  Vgv*'**'^ 

*  Stout.  >    Baldwin.  *    Home.  *  Davidson. 


{f^  (9)  Religion  consists  in  the  feeling  of  absolute  de- 


pendence.* •^. 


rT    (10)  Religion  is  a  desire  manifested  by  prayer,  sacri 
^  fice,  and  faith.*  wv*^ 

(11)  Religion  is  a  faculty  of  the  mind  by  which,  inde- 


^<> 


,  pendently  of  the  senses  and  of  reason,  man  is  able  V*' 
to  p)erceive  the  Infinite.'  i** 


/'/i 


5.  Show  that  a  definition  is  always  relative  to  the  purpose 
entertained. 

6.  What  are  the  predicables?  Distinguish  between  a  'dif- 
ferentia* and  an  'accident.' 

7.  Write  out  a  list  of  at  least  five  words  or  phrases  which 
you  regard  as  catch-words  which  need  definition. 

8.  Look  up  the  platforms  of  the  various  political  parties  for 
words  which  seem  to  you  to  need  definition. 

CHAPTER  VII 

1.  Distinguish  between  'assertions'  and  'propositions.' 
What  was  the  error  of  the  more  formal  logic  of  the  past? 

2.  Show  that  judgment  is  a  process  of  interpretation  end- 
rm  ing  in  an  assertion. 

Is.  Bring  out  by  at  least  three  examples  the  genetic  side  oil 
^    judgment.  J 

■^  4.  Show  that  the  world  as  we  experience  it  is  a  product  of 
past  mental  activity. 
6.  In  what  sense  are  there  levels  of  judgment?   Give  cases 
to  prove  the  increasing  complexity  of  judgment  as  we 
pass  from  concrete  things  to  principles. 

6.  What  two  aspects  are  there  to  every  judgment? 

7.  Distinguish  between  the  actual  operation  of  judging  and 
its  verbal  expression.  What  is  the  purpose  which  con- 
trols language? 

8.  What  is  meant  by  the  'universe  of  discourse'?  Indicate 
the  reason  for  its  importance  in  the  proper  interpretation 
of  propositions. 

>  Schleiennocher.  '  Feuerbach.  *  Max  MUller. 


QUESTIONS  AND  EXERCISES  317 

CHAPTER  VIII 

1.  Distinguish  between  'categorical,'  'hypothetical,'  and 
'disjunctive'  propositions. 

2.  What  is  meant  by  the  'quantity'  of  propositions?  By 
their  'quality'? 

3.  Throw  the  following  propositions  into  logical  form, 
give  the  letter  that  symbolizes  the  quantity  and  quality, 
and  state  the  distribution  of  the  terms:  — 

(1)  Not  all  who  are  called  are  chosen. 

(2)  Few  were  saved. 

(3)  None  of  the  planets  except  the  earth  is  inhabited. 

(4)  He  can't  be  wrong  whose  life  is  in  the  right. 

(5)  More  haste  less  speed. 

(6)  All  politicians  are  not  dishonest. 

(7)  Only  noble  deeds  deserve  praise. 

(8)  Mercy  but  murders,  pardoning  those  that  kill. 

(9)  No  one  is  always  happy, 

(10)  Only  some  citizens  have  the  right  to  vote. 

4.  Explain  why  negative  propositions  always  distribute  the 
predicate. 

5.  Apply  the  graphical  method  to  the  four  kinds  of  cate- 
gorical propositions. 

6.  What  is  the  purpose  underlying  the  logical  manipulation 
of  propositions. 

CHAPTER  IX 

1.  What  is  immediate  inference? 

2.  Be  prepared  to  write  down  and  explain  the  Square  of 
Opposition. 

3.  What  propositions  are  true,  false,  or  doubtful*  — 

(1)  when  A  is  false;        (3)  when  I  is  false; 

(2)  when  E  is  false;         (4)  when  0  is  false? 
^ll^What  is  the  simplest  proposition  which  must  be  esjab- 
^^Vlished  in  order  to  disprove  the  following  statements:  — 

(1)  All  men  desire  wealth. 

(2)  No  man  is  perfectly  happy. 

(3)  Some  knowledge  is  not  of  any  value. 

(4)  Pain  alone  is  evil. 

(5)  All  is  not  lost.i 

>  Creighton. 


818  QUESTIONS  AND  EXERCISES 

5.  Give  the  converse,  the  obverse,  and  the  contrapositive 
of  each  of  the  following  propositions:  — 

(1)  Only  a  fanatic  believes  in  panaceas. 

(2)  Uneasy  lies  the  head  that  wears  a  crown. 

(3)  No  men  are  always  happy. 

(4)  Most  of  the  nations  were  unprepared. 

(5)  None  but  the  industrious  deserve  to  succeed. 

(6)  All  men  are  mortal. 

(7)  Discontent  is  frequently  a  symptom  of  inefficiency. 

(8)  Children  are  noisy  on  rainy  days. 

6.  By  what  process  do  we  pass  from  each  of  the  following 
propositions  to  the  next? 

(1)  No  knowledge  is  useless. 

(2)  No  useless  thing  is  knowledge. 

(3)  All  knowledge  is  not  useless. 
0)  All  knowledge  is  useful. 

'V.  (5)  What  is  not  useful  is  not  knowledge. 

(6)  What  is  useless  is  not  knowledge. 

(7)  No  knowledge  is  useless.^ 

7.  Test  the  following  arguments  by  obversion  and  con- 
version: — 

(1)  When  we  hear  that  all  the  righteous  people  are 
happy,  it  is  hard  to  avoid  exclaiming.  What!  are 
all  the  unhappy  persons  we  see  to  be  thought  un- 
righteous? 

(2)  If  a  man  who  has  been  accustomed  to  enjoy  lib- 
erty cannot  be  happy  in  the  condition  of  a  slave, 
does  it  follow  that  a  man  who  has  not  been  accus- 
tomed to  Uberty  can  be  happy  as  a  slave? 

CHAPTER  X 

1.  How  did  Aristotle  define  the  syllogism?    What  was  the 

germ  of  his  invention? 
2?  What  is  the  Dictum  de  omni  et  nvUo  ? 

3.  Be  prepared  to  demonstrate  each  Of  the  rules  of 
syllogism. 

4.  What  criticism  would  you  be  inclined  to  pass  upon  the 
syllogism  when  treated  very  formally? 

5.  Select  and  name  the  various  propositions  and  terms  g{ 

>  Jevons. 


I 


QUESTIONS  AND  EXERCISES  319 

the  syllogism  in  the  following  informally  stated  argu- 
ments. Then  reconstruct  them  so  as  to  make  formally 
correct  syllogisms: —         ^^  \jXy*'>*^ 

(1)  All  leeches  must  be^ue  worms;  for  all  annelids 
are  worms,  (und  leeches  areanneUds^^M*»»  V"***?** 

(2)  Caterpillars  have  true  legs;  worms  do  not;  an5  so 
caterpillars  are  not  worms.  -<-<»>^  ^ 

(3)  Amphibians  are  not  reptilesrsmce  they  breathe  ***^ 
by  gills  in  the  larval  stage,  and  reptiles  do  not-^v^-iu^i 

6.  If  either  premise  of  a  syllogism  is  0,  what  must  the  other 
be? 

7.  Prove  that  there  must  be  in  the  premises  one  more  dis- 
tributed term  than  in  the  conclusion. 

8.  Prove  that  if  one,  but  only  one,  premise  is  negative,  and 
both  premises  are  universal,  they  will  between  them  dis- 
tribute three  terms. 

9.  Put  the  following  argument  into  syllogistic  form:  — 

How  can  any  one  maintain  that  pain  is  always  an  evil,^^'^  • 
who  admits  that  remorse  involves  pain,  and  yet  may 
sometimes  be  a  real  good?      •  Srtv^  Xjuul^^/u  '  S»)<n 

%       \        OmJ       ^  "-hAAA. 

>     CHAPTER  XI        cS<rr>^^^^^u^    l':.OLjir 

1.  Arrange  the  following  arguments  in  logical  order.  Name 
the  figure  of  the  syllogism,  and  if  the  argument  is  in- 
valid, state  the  formal  fallacy  involved:  —  ^ 

(1)  All  M  is  P;  no  itf  is  S;  therefore  no  S  is  P.  "^-^ 

(2)  No  P  is  M;  some  S  is  M;  therefore  some  S  isj'^'*^ 
not  P. 

(3)  Some  useful  metals  are  becoming  rarer;  iron  is  a  ,5!  k^  * 
useful  metal,  and  is  therefore  becoming  rarer.  ""^       . 

(4)  None  but  whites  are  civilized;  the  ancient  Ger-  j  tyix'  '* 
mans  were  white;  therefore  they  were  civilized. 

(5)  Since  the  virtuous  alone  are  happy,  he  must  be  ^^  \ 
virtuous  if  he  is  happy,  and  he  must  be  happy  if  '  ^  ->/^'l 
he  is  virtuous. 

(6)  It  is  not  true  that  a  man  cannot  do  a  great  work  ^^  '  f 
without  a  strong  physique;  for  the  philosopher  "^^^'j 
Kant  did  a  great  work  and  his  physique  was  any-  "^qP^ 
thing  but  strong.  ^y^  ^P"- 


Taylor. 


'^d 


20         ^  QUESTIONS  AND  EXERCISES 

'^(7)  Onjy  animals  are  sentient  beings;  fishes  are  ani- 
JBtals;  therefore  fishes  are  sentient  beings. 
I   ft'    (8)  Good  men  write  good  books;  this  is  a  good  book; 
^  therefore  its  writer  was  a  good  man. 
.  f\9)  Every  book, is  liable  to  error;  every  book  is  a  hu- 
/(v  man  production;  therefore  all  human  productions 

are  liable  to  error. 

2.  Write  out  the  sixty-four  moods  of  the  syllogism  and 
strike  out  the  fifty-three  invalid  ones. 

3.  Prepare  to  prove  the  special  canons  of  each  of  the  four 
figures. 

4.  Make  a  syllogism  in  £  7  0,  any  figure,  and  exhibit  the 
conversions  necessary  to  accommodate  it  to  each  of  the 
other  figures.^ 

5.  Why  is  the  first  figure  usually  considered  the  standard 
figure? 

6.  Supply  premises  for  the  following  conclusions:  — 

(1)  Some  politicians  are  not  dishonest. 

(2)  The  moon  tends  to  fall  to  the  earth. 

(3)  Banks  sometimes  fail. 

(4)  Some  logicians  art  not  good  reasoners. 

CHAPTER  XII 

1.  Complete  the  following  arguments,  determine  their 
mood  and  figure,  and  decide  whether  they  are  valid:  — 

(1)  Blessed  are  the  meek,  for  they  shall  inherit  the 
earth. 

(2)  Only  the  good  are  fit  to  die,  therefore  capital  pun- 
ishment is  wrong. 

(3)  Let  us  meet  her.  Why?  They  say  she's  mad. 

(4)  Because  thou  art  virtuous,  shall  there  be  no  more 
cakes  and  ale? 

(5)  None  but  material  bodies  gravitate;  therefore  air 
is  a  material  body. 

2.  Construct  an  enthymeme  of  each  of  the  three  orders. 

3.  Construct  a  complex  argument  containing  a  prosyl- 
logism  and  an  episyllogism. 

4.  Show  why  all  the  premises  except  the  first  must  be  uni- 
versal in  an  Aristotelian  Sorites. 

»  Taylor. 


QUESTIONS  AND  EXERCISES  321 

5.  Prove  by  graphical  methods  that  in  the  Goclenian  So- 
rites the  first  premise  alone  can  be  negative,  and  the 
last  alone  particular. 

6.  What  is  an  extra-syllogistic  argument?  Contrast  it  with 
syllogistic  inference. 

7.  Why  are  fallacies  more  apt  to  exist  in  condensed  argu- 
ments than  in  expansed  ones? 

CHAPTER  Xin 

1.  Determine  which  of  the  following  give  valid  conclusions 
and  which  do  not;  in  case  of  invalidity,  name  the  fallacy: 

(1)  If  the  door  were  locked,  the  horse  would  not  be 
stolen;  but  the  horse  is  not  stolen,  therefore  the 
door  must  have  been  locked. 

(2)  If  all  men  were  capable  of  perfection,  some  would 
have  attained  it;  but  none  having  done  so,  none 
are  capable  of  it. 

(3)  If  every  ghost  story  is  to  be  believed,  we  must 
accept  the  general  standpoint  of  the  spiritualists; 
but  we  cannot  accept  their  general  standpoint; 

^^^Jherefore  we  cannot  believe  ghost  stories.^ 

(4)  *lf  Be  has  not  studied,  he  will  fail  in  the  examina- 
tion.' With  this  proposition  as  a  major  premise, 
what  can  be  inferred  if  we  take  as  minor  premise: — 

(1)  He  has  not  studied. 

(2)  He  will  fail. 

(3)  He  will  not  fail. 

(4)  He  has  studied. 

(5)  If  it  becomes  colder  to-night,  there  will  be  a  frost; 
but  it  will  not  become  colder  to-night;  therefore 
there  will  be  no  frost. 

2.  Does  the  categorical  or  the  hypothetical  syllogism  seem  to 
you  the  simpler?   Which  of  the  two  stresses  denotation? 

3.  Where  is  the  source  of  danger  in  the  disjunctive  syllo- 
gism? 

4.  Work  out  a  dilemma  on  some  subject  of  debate. 

5.  Examine  the  following  arguments :  — 

(1)  It  is  either  raining  or  not  raining;  it  is  not  raining; 
therefore  it  is  raining. 

1  Aikins. 


322  QUESTIONS  AND  EXERCISES 


/i 


(3VNo  honest  man  can  advocate  a  change  in  the 
y  creed  of  his  church;  for  he  must  either  believe  it 
or  not  beUeve  it;  and  if  he  believes  it,  he  cannot 
honestly  help  to  change  it,  while  if  he  does  not 
believe  it  he  cannot  honestly  belong  to  the  church 
at  all. 
^  (3)  In  order  to  move,  a  body  must  move  either  in  the 

/  place  where  it  is  or  in  the  place  where  it  is  not. 

''  .     But  it  cannot  move  in  the  place  where  it  is,  since 
\    that  place  is  already  occupied.    Neither  can  it 
move  in  the  place  where  it  is  not.  Motion  is  there- 
fore imp)ossible. 
(4)  If  transportation  is  not  felt  as  a  severe  punishment, 
Mt  is  in  itself  ill-suited  to  the  prevention  of  crime; 
I  V\  ^  »A    if  it  is  so  f^^t,  much  of  its  severity  is  wasted,  from 
J      r   /f    \  its  taking  place  at  too  great  a  distance  to  affect 
tr  ^  ^^he  feeling,  or  even  come  to  the  knowledge,  of  most 
those  whom  it  is  designed  to  deter;  but  one  or 
the  other  of  these  must  be  the  case;  therefore  trans- 
'^'  ^^      portation  is  not  calculated  to  answer  the  purpose 
\A  8^  of  preventing  crime. 


W 


<f,m. 


^ 


CHAPTER  XIV 


1.  Distinguish  between  a  'sophism'  and  a  'fallacy.* 

2.  Review  the  formal  fallacies. 

3.  Be  able  to  classify  material  fallacies  under  two  appro- 
priate headings. 

4.  Look  up  advertisements  to  see  whether  you  can  find 
some  examples  of  amphiboly. 

5.  Give  an  example  of  the  fallacy  of  accident.  Also  of  the 
converse  fallacy  of  accident. 

6.  Explain  the  difference  between  'begging  the  question' 

and  'irrelevant  conclusion.* 

7.  Give  an  example  each  of  Argumentum  ad  hominem,  Ar- 
gumentum  ad  populum,  Argumentum  ad  ignorantiam, 
and  Argumentum  ad  vericundiam. 

8.  Note  and  classify  the  fallacies  in  the  following  argu- 
ments :  — 

(1)  A  monopoly  of  the  sugar-refining  business  is  bene- 
ficial to  the  sugar-refiners;  and  of  the  corn  trade  to 


QUESTIONS  AND  EXERCISES  323 

the  corn-growers;  and  of  silk  manufacture  to  the 
silk- weavers;  and  of  labor  to  the  laborers.    Now,  d>»wj,,_  £ 
all  these  classes  of  men  make  up  the  whole  com-        /       ^ 
munity.    Therefore  a  system  of  restrictions  upon 
competition  is  beneficial  to  the  community.* 

(2)  Any  student  in  college  would  stand  higher  in  his  ^^*^V**^*  * 
class  if  he  received  higher  marks;  hence,  if  all  ■^[T/?**-**' 
marks  were  raised  ten  per  cent  every  man  would  [ojl  *^ 
stand  nearer  the  head  of  his  class.  ^^^'*"'* 

(3)  Since  attending  that  mass  meeting  of  students,  I  *^^^llaA 
have  had  no  confidence  in  decisions  reached  in 

that  way. 

(4)  Wine  is  a  stimulant;  therefore,  in  every  case  where  AMa  ***> 
a  stimulant  is  harmful,  wine  is  harmful. 

(5)  We  know  that  God  exists,  because  the  Bible  tells     /^ 
usso;and  we  know  that  whatever  the  Bible  aflSrms  IjI 

is  true,  because  it  is  of  divine  origin.  J^^ 

(6)  A  miracle  is  incredible  because  it  contradicts  the         ,,     •• 
laws  of  nature.  ^^hU^t 

(7)  We  charge  him  (King  Charles  the  %m»mit)  with 
having  broken  his  coronation   oath,  and  we  are  « 
told  that  he  kept  his  marriage  vows;  we  accuse      j  y'f*'^^^ 
him  of  having  given  up  his  people  to  the  merciless       ^^^  ^  * 
infliction  of  the  most  hot-headed  and  hard-heartea 

of  prelates,  and  the  defense  is  that  he  took  his  little 
son  on  his  knee  and  kissed  him;  we  censure  him  for 
having  violated  the  articles  of  the  Petition  of 
Rights,  after  having  for  a  good  and  valuable  con- 
sideration promised  to  observe  them,  and  we  are 
informed  that  he  was  accustomed  to  hear  prayers 
at  six  o'clock  in  the  morning. 

What  fallacy  does  Macaulay  refer  to  in  this 
passage?  ^ 

(8)  If  it  is  fated  that  you  die,  you  will  die  whether /^^  9  ''^'t 
you  call  in  a  doctor  or  not,  and  if  it  is  fated  that      >  ^  * 
you  will  recover,  you  will  recover  whether  you  call       7 

in  a  doctor  or  not.  But  it  must  be  fated  either  that 
you  die  or  that  you  recover.  Therefore,  you  will 
either  die  or  recover,  whether  you  call  in  a  doctor 
or  not. 

>  Hyslop.  '  Russell. 


324  QUESTIONS  AND   EXERCISES 

(r(9)  Every  incident  in  the  narration  is  probable;  hence, 
^»*         the  narrative  is  probable. 
M>r      (10)  The  growing  size  of  London  bodes  evil  to  England 
\,t\  because  London  is  the  heart  of  England,  and  a 

^  swollen  heart  is  a  sign  of  disease. 

9.  "The  President  of  the  United  Staites  can  veto  bills,  but 

he  can  only  veto  a  bill  as  a  whole.  It  is  therefore  not 

/    uncommon  for  Congress  to  tack  on  to  a  bill  which  the 

y      President  feels   bound   to  pass  a  clause   containing  a 

,  measure  to  which  it  is  known  that  he  objects."    Show 

^ti^l  that  this  is  a  practical  application  of  a  fallacy. 

10.  "One  of  the  most  remarkable  examples  of  fallacy  is 
>               furnished  by  the  political  theory  of  Hobbes  and  Rous- 

y^  seau,  known  as  the  theory  of  the  'social  compact.'  We 
«  ^^1    yare  supposed  bound  by  the  promise  entered  into  by  our 
y  ijf^    ancestors  before  society  was  called  into  existence;  but 
\       there  is  no  such  thing  as  an  obligatory  promise  until  so- 
ciety has  been  formed."  What  important  assumption  is 
made  in  this  criticism  of  the  compact-theory? 

11.  "H«w.  is  it  that  we  hear  so  much  of  French  immorality, 
and  nothing,  or  next  to  nothing,  of  Italian?  How  is  it 
that,  in  France,  we  have  heard  so  much  of  English  bar- 

^  \        barity  and   cruelty,  whilst    the   accounts  of   Turkish 
v>^^' cruelty  were  received  with  the  smile  of  incredulity  or 
K         the  shrug  of  indiflference?"  ^  What  tendency  to  fallacy 
does  this  quotation  illustrate?  Give  other  instances. 

12.  "Achilles  and  a  tortoise  run  a  race  together.  Achilles 
runs  ten  times  quicker  than  the  tortoise,  and  accepts,  in 
consequence,  a  handicap  of  a  hundred  yards.  Under  these 
Mionditions,  argued  Zeno,  Achilles  will  never  overtake  the 

f^'aortoise;  for  when  the  tortoise  has  gone  ten  yards,  Achilles 
^  will  still  be  ten  yards  behind  him.  When  these  ten 
yards  are  caught  up,  the  tortoise  will  still  be  ahead  by 
one  yard.  When  this  yard  is  caught  up,  one-tenth  of  a 
yard  will  still  separate  them,  and  so  on  indefinitely. 
Achilles,  then,  though  he  will  be  continually  drawing 
nearer  to  the  tortoise,  will  never  actually  overtake  him." 
How  would  you  criticize  this  argument? 

I  HammertoD,  French  and  English. 


QUESTIONS  AND  EXERCISES  826 

FURTHER  EXAMPLES  OF  DEDUCTIVE 
ARGUMENTS 

CHAPTERS  X  TO  XIV 

1.  The  right  should  be  enforced  by  law;  the  exercise  of  the 
suffrage  is  a  right,  and  should  therefore  be  enforced  by 
law. 

2.  Every  rule  has  exceptions;  this  is  a  rule,  and  therefore 
has  exceptions;  therefore  there  are  some  rules  that  have 
no  exceptions, 

3.  Is  a  stone  a  body?  Yes.  Then  is  not  an  animal  a  body? 
Yes.  Are  you  an  animal?  I  think  so.  Ergo,  you  are  a 
stone,  being  a  body. 

4.  His  imbecility  of  character  might  have  been  inferred 
from  his  proneness  to  favorites;  for  all  weak  princes 
have  this  failing. 

5.  At  the  time  of  the  Galveston  flood  men  worked  sixteen 
hours  a  day;  hence,  to  talk  of  an  eight-hour  day  as  a 
necessity  for  the  working  classes  is  absurd.^ 

6.  Haste  makes  waste,  and  waste  makes  want;  therefore 
a  man  never  loses  by  delay. 

7.  A  college  education  does  not  pay  for  most  self-made 
Americans  have  succeeded  without  it. 

8.  All  material  bodies  impress  the  senses;  mind  does  not 
impress  the  senses.    What  is  the  inference?  ^ 

9.  Art  is  not  fostered  by  money;  for  a  true  artist  would  prac- 
tice his  art  for  its  own  sake,  and  a  bad  artist  should  not 
be  encouraged. 

10.  Wealth  is  in  proportion  to  value,  value  to  efforts,  efforts  , 
to  obstacles;  therefore  wealth   is  in  proportion  to  ob- 
stacles. 

11.  For  those  who  are  bent  on  cultivating  their  minds  by 
diligent  study,  the  incitement  of  academic  honors  is 
unnecessary;  and  it  is  ineffectual  for  the  idle  and  such 
as  are  indifferent  to  mental  improvement;  therefore  the 
incitement  of  academic  honors  should  be  abolished. 

12.  It  is  impossible  to  be  a  good  shot  without  having  a 

"  Jones.  *    Taylor. 


Bit  QUESTIONS   AND  EXERCISES 

steady  hand;   John  has  a  steady  hand;  he  is  capable, 
I  therefore,  of  becoming  a  good  shot. 

fc^*  ^ft^    13.  The  theory  of  evolution  is  not  true,  for  it  was  not  ac- 
yf^*^  cepted  by  Agassiz  or  by  Gladstone ;  moreover,  you  cannot 

accept  this  doctrine,  for  it  is  disclaimed  by  the  au- 
thorities of  your  church.* 
/^y-*^  14.  The  end  of  a  thing  is  its  perfection;  death  is  the  end  of 
'!'  -  life;  therefore  death  is  the  perfection  of  life. 

15.  Improbable  events  happen  almost  every  day;  but  what 
^     **  happens  almost  every  day  is  a  very  probable  event; 

,  therefore  improbable  events  are  very  probable  events. 

^  .     1  16.  No  evil  should  be  allowed  that  good  may  come  of  it;  all 
X^i'^y^  punishment  is  an  evil;  therefore  no  punishment  should 

^  be  allowed  that  good  many  come  of  it. 

^    ^    17.  Why  does  a  ball,  when  dropped  from  the  masthead  of  a 
ship  in  full  sail,  fall,  not  exactly  at  the  foot  of  the  mast, 
but  nearer  to  the  stern  of  the  vessel? 
18.  Written  examinations  are  not  absolutely  fair  tests  of  a 
^••)*     •  -        student's  scholarship  —  much  less  of  his  industry  and 
S     tf^  intelligence.     It  is  therefore  wrong  to  base  his  grade 

upon  them, 
y^'^^r  19.  A  vacuum  is  impossible,  for  if  there  is  nothing  between 
•^ *^  two  bodies  they  must  be  in  contact. 

^    •    20.  "They  tell  us  that  we  are  weak,  unable  to  cope  with  so 

S(^<*^J^  ■       formidable  an  adversary ;  but  when  shall  we  be  stronger  ?  *  * 

\^j^\.  Nothing  is  better  than  wisdom;  dry  bread  is  better  than 

>W'l  nothing;  therefore  dry  bread  is  better  than  wisdom. 

1 4»^  22.  Whoever  believes  this  is  a  heretic;  so  that  you  are  no 


heretic,  for  you  do  not  believe  this. 

23.  If  a  man  is  educated,  he  does  not  want  to  work  with  his 
hands;  consequently,  if  education  is  universal,  industry 
will  cease. 

24.  "  The  railroads  have  usually  acted  upon  the  apparent  pol- 
icy that  it  is  none  of  the  public's  business  whether  they 
are  overcapitalized  or  not.  It  remained  for  the  counsel 
for  the  N.  and  N.  Railroad,  a  road  notorious  for  its 
stock-watering  operations,  publicly  to  declare  —  in  form 
of  a  question,  it  is  true,  but  none  the  less  bluntly  —  the 
railroad  position.  If  the  N.  and  N.  'charges  reasonable 
rates,'  demands  its  counsel,  'what  is  it  to  the  public 

'  Creigbton. 


QUESTIONS  AND  EXERCISES  827 

whether  its  capitalization  be  high  or  low?'"    What 

assumption  is  involved  in  this  question?  * 

25.  Berkeley's  Theory  of  the  Non-Existence  of  Matter  is 

-*.     palpably  absurd,  for  it  is  impossible  even  to  place  one's 

'«    Ij^',  foot  on  the  ground  without  experiencing  the  resistance 

jT^      of  matter, 

^   26.  I  have  no  hesitation  in  saying  that  the  proposition,  how- 
ever good  in  theory,  is  in  practice  utterly  absurd. 

27.  Epimenides  the  Cretan  says  that  "all  Cretans  are  liars," 
but  Epimenides  is  himself  a  Cretan;  therefore  he  is  him- 
self a  liar.  But  if  he  be  a  liar,  what  he  says  is  untrue,  and 
consequently  the  Cretans  are  veracious;  but  Epimenides 
is  a  Cretan,  and  therefore  what  he  says  is  true;  hence  the 
Cretans  are  liars,  Epimenides  is  himself  a  liar,  and  what 
he  says  is  untrue.  Thus  we  may  go  on  alternately 
proving  that  Epimenides  and  the  Cretans  are  truth- 
ful and  untruthful. 

28.  There  exist  many  difiFerences  of  opinion  and  much  un- 
certainty with  regard  to  many  questions  connected  with 
geology;  consequently  geology  is  not  a  science,  and  any 
arguments  which  assume  the  truth  of  geological  theories 
must  invariably  be  regarded  with  considerable  sus- 
picion. 

29.  Personal  deformity  is  an  affliction  of  nature ;  disgrace  is  not 
an  affliction  of  nature;  personal  deformity  is  not  a  disgrace. 

30.  Testimony  is  a  kind  of  evidence  which  is  very  likely  to  be 
false;  the  evidence  on  which  most  men  believe  that 
there  are  pyramids  in  Egypt  is  testimony;  therefore  the 
evidence  on  which  most  men  believe  that  there  are  pyra- 
mids in  Egypt  is  very  likely  to  be  false. 

81.  Why  should  any  but  professional  moralists  trouble  them- 
selves with  the  solution  of  moral  difficulties?  For,  as 
we  resort  to  a  physician  in  case  of  any  physical  disease, 
so,  in  the  case  of  any  moral  doubt  or  any  moral  disor- 
ganization, it  seems  natural  that  we  should  rely  on 
the  judgment  of  some  man  especially  skilled  in  the 
treatment  of  such  subjects. 

82.  "A  asserts  with  incorrigible  optimism  that  'without  too 
much  you  cannot  have  enough  of  anything.  Lots  of 
inferior  books,  lots  of  bad  statues,  lots  of  dull  speeches, 

>  Bode. 


>^ 


128  QUESTIONS  AND  EXERCISES 

of  tenth-rate  men  and  women,  as  a  condition  of  the  few 
precious  specimens  in  either  kind  being  realized.'  As 
the  condition,  yes;  but  as  the  cause,  no.  We  can  never 
have  the  precious  things  in  Uterature  merely  by  adding 
to  the  multitude  of  cheap  things."  ^ 
83.  "An  abimdant  stream  divides  two  limits  of  one  prop- 
erty .  .  .  and  over  this  stream  stood  a  bridge;  and  at 
the  head  of  it  a  gallows,  over  which  were  appointed  four 
judges  to  decide  according  to  the  law  established  by  the 
lord  of  the  stream,  the  bridge,  and  the  territory.  The 
law  ran  in  this  wise:  *If  any  one  shall  pass  over  this 
/J.  bridge  from  one  side  to  the  other,  he  must  first  swear  as 
Vf  *  to  whence  he  comes  and  on  what  business  he  is  bound, 
and  if  he  swear  truly,  he  must  be  allowed  to  go;  but  if 
he  swear  falsely,  he  shall  on  that  account  die  by  hanging 
on  the  gallows  which  is  there;  and  that  without  remis- 
sion whatever.'  This  law  and  its  stern  conditions  being 
known,  many  went  over;  and  as  soon  as  it  was  perceived 
that  they  swore  truly,  the  judges  allowed  them  to  pass 
freely.  It  happened,  however,  that  on  swearing  one 
man,  he  took  the  oath  and  declared  that  he  was  going 
to  die  on  that  gallows,  and  that  he  had  no  other  business. 
The  judges  consulted  the  terms  of  the  oath,  and  said: 
'If  we  allow  that  man  to  go  free,  he  has  sworn  falsely,  and 
according  to  the  law  he  ought  to  die;  and  if  we  hang  him, 
•      •  the  oath  that  he  was  going  to  hang  on  that  gallows  was 

true,  and  according  to  the  same  law  he  ought  to  be  free.' "  ' 
S     34.  We  must  either  gratify  our  vicious  propensities,  or  re- 
tr  sist  them;  the  former  course  will  involve  us  in  sin  and 

/\  misery;  the  latter  requires  self-denial;  therefore  we  must 

either  fall  into  sin  and  misery  or  practice  self-denial. 
S5.  "America  has  still  a  long  vista  of  years  stretching  before 
her  in  which  she  will  enjoy  conditions  far  more  auspi- 
.    cious  than  any  European  country  can  count  upon.    And 
>  \     that  America  marks  the  highest  level,  not  only  of  ma- 
.  terial   well-being,   but   of   intelligence   and   happiness, 

_Jf  which  the  race  has  yet  attained,  will  be  the  judgment  of 

\  those  who  look,  not  at  the  favored  few  for  whose  bene- 

fit the  world  seems  hitherto  to  have  framed  its  institu- 
tions, but  at  the  whole  body  of  the  people."  ' 

>  Creighton.  *  From  Don  Quixote.  *  James  Bryce. 


-v^ 


QUESTIONS  AND   EXERCISES  329 

36.  This  is  a  party  measure  and  therefore  we  must  vote  for  it.  ^^llj^* 
87.  "Philosophy  bakes  no  bread."    Then  why  waste  timel^  r 

upon  it?  '^^  ^ 

38.  I  oppose  this  bill  because  it  involves  an  infringement  of 

the  rights  of  the  liberty-loving  citizens  of  this  State. 

CHAPTER  XV 

1.  Why  are  'induction*  and  'deduction*  somewhat  mis- 
leading terms? 

2.  Show  how  the  perspective  of  logic  has  shifted  from  age 
to  age. 

3.  Distinguish  between  the  'logic  of  consistency*  and  the 
'logic  of  investigation.' 

4.  Look  up  an  instance  of  systematic  investigation,  such 
as  can  be  found  in  Darwin,  Newton,  Faraday,  etc.,  and 
analyze  the  various  logical  steps  taken. 

5.  What  are  the  three  elements  which  can  be  distinguished 
in  investigation? 

6.  What  is  involved  in  generalization?  Exemplify  the  pas- 
sage from  the  particular  to  the  general. 

7.  What  is  meant  by  an  'internal  relation'?  How  does  the 
relation  between  a  sign  and  that  which  it  signifies  diflFer 
from  association? 

8.  Do  animals  generalize? 

9.  Discuss  the  statement,  assigned  to  Wundt,  that  "ani- 
mals never  reason  and  man  seldom." 

10.  Is  the  tendency  to  test  generalizations  as  characteristic 
of  man  as  the  tendency  to  generalize  ilself  ? 

CHAPTER  XVI 

1.  What  do  you  understand  by  science?  What  are  some  of 
its  guiding  ideals? 

2.  Look  up  the  history  of  some  science  with  which  you  are 
fairly  familiar,  and  ask  yourself  what  its  growth  consists 
in. 

8.  Why  is  analysis  so  basic  for  science? 

4.  Point  out  the  significance  of  technique  and  instru- 
ments. Are  they,  in  your  opinion,  sometimes  overesti- 
mated at  the  exi>ense  of  mental  factors? 


330  QUESTIONS  AND   EXERCISES 

5.  What  is  the  nature  of  experimentation?    Indicate  the 
'         advantages  of  experimentation  as  against  passive  ob- 
servation. 

6.  Find  and  analyze  at  least  two  important  experiments  in 
each  of  the  following  sciences:  physics,  chemistry,  biology, 
and  psychology. 

7.  What  other  methods  have  grown  up  in  modern  investi- 
gation? 

8.  What  reaction  has  science  had  upon  common-sense 
thinking? 

9.  Become  acquainted  with  the  mental  life  of  at  least  one 
great  scientist. 

CHAPTER  XVn 

1.  What  principle  should  guide  induction? 

2.  What  is  meant  by  'mere  speculation,'  and  why  is  it  con- 
demned? 

8.  State  some  of  the  mental  and  physical  conditions  of  ac- 
curate observation. 

4.  Show  that  perception  is  a  process  involving  associated 
ideas  as  well  as  sensations. 

5.  What  are  the  causes  of  mal-observation  and  non-ob- 
servation in  the  following  cases? 

(1)  A  straight  stick  partly  immersed  in  water  seems  to 
be  bent. 

(2)  The  sun  seen  through  a  fog  sometimes  appears 
red. 

(3)  Patients  often  seem  to  feel  pain  in  amputated 
limbs. 

(4)  A  rearrangement  of  the  furniture  in  a  room  is  often 
unnoticed. 

(5)  There  are  marked  differences  in  what  the  ordinary 
good  observer,  the  artist,  and  the  botanist  see  in 
a  flower. 

(6)  Silas  Mamer  mistook  Effie's  hair  for  the  lost  gold. 

(7)  Looking  at  one's  watch  and  not  knowing  the  time 
a  moment  later. 

•  (8)  Shooting  a  man  for  a  deer  when  hunting  in  the 
woods.* 

>  Jones. 


QUESTIONS  AND  EXERCISES  331 

6.  Seek  for  cases  of  erroneous  perception  in  your  own  exg 
perience,  and  try  to  explain  them. 

7.  Is  memory  a  direct  intuition  of  the  past? 

8.  How  do  the  sciences  try  to  eliminate  errors  due  to 
memory?  Why  cannot  this  be  done  in  the  courts  of  law? 

9.  Present  at  least  five  instances  of  erroneous  memory. 
10.  How  is  the  relevancy  of  facts  determined? 

CHAPTER  XVIII 

1.  What  is  an  hypothesis?  And  what  are  its  conditions? 

2.  Show  by  examples  that  hypotheses  always  arise  in  answer 
to  problems. 

8.  Criticize  the  Baconian  view  of  science. 

4.  What  do  men  like  Ernst  Mach  and  Wilhelm  Ostwald 
mean  by  hypotheses  when  they  are  inclined  to  urge 
scientists  to  avoid  them  so  far  as  possible? 

5.  Take  any  two  instances  of  hypotheses  which  have  be- 
come accepted  theories  and  show  that  only  the  expert 
could  have  thought  of  them. 

6.  Distinguish  between  the  'intuitive'  and  the  'reflective' 
type  of  mind.  Are  these  types  easily  recognizable  in 
practice? 

7.  Name  three  famous  men  who  represent,  on  the  whole, 
the  intuitive  type,  and  three  who  are  quite  clearly  of  the 
reflective  type. 

8.  What  is  the  relation  between  observation  and  the  pos- 
session of  an  hypothesis? 

9.  Explain  the  nature  of  the  development  of  an  hypothesis. 
Why  does  such  development  require  systematic  knowl- 
edge? 

10.  Is  a  barren  hypothesis  the  same  as  an  unverifiable  one? 

11.  Distinguish  between  'proof  and  'verification.' 

12.  Why  is  analogy  such  an  important  source  of  hypotheses? 

13.  What  is  meant  by  'false  analogy'?  Give  at  least  five 
examples. 

14.  Take  any  two  important  theories  generally  accepted 
to-day  and  study  their  history.  Exactly  what  was  the 
problem  which  they  were  developed  to  explain? 

15.  What  danger  is  there  in  arguing  from  the  assumption 
that  society  is  an  organism? 


332  QUESTIONS  AND  EXERCISES 

^  CHAPTER  XIX 

Analyze  the  following  examples  of  inductive  argumenta- 
tion, and  state  the  method  implied.  Do  the  facts  seem  to  you 
to  be  suflScient  to  found  a  rule  upon? 

1.  It  may  be  a  coincidence  merely;  but,  if  so,  it  is  remark- 
ably strange  that  while  the  chloroform  has  not  changed, 
while  the  constitutions  of  the  patients  have  not  changed, 
where  the  use  of  the  inhaler  is  the  rule,  there  are  fre- 
quent deaths  from  chloroform;  whilst  in  Scotland  and 
Ireland,  where  the  use  of  the  inhaler  is  the  exception, 
deaths  are  proportionally  rare.^ 

2.  Sir  Charles  Lyell,  by  studying  the  fact  that  the  river 
Ganges  yearly  conveys  to  the  ocean  as  much  earth  as 
would  form  sixty  of  the  great  pyramids  of  Egypt,  was 
enabled  to  infer  that  the  ordinary  slow  causes  now  in 
operation  upon  the  earth  would  account  for  the  immense 
geological  changes  that  have  occurred,  without  having 
recourse  to  the  less  reasonable  theory  of  sudden  catas- 
trophes. 

8.  Take  a  bottle  of  charged  water,  slightly  warmer  than 
a  given  temperature  registered  by  the  thermopile,  and 
mark  the  deflection  it  causes.  Then  cut  the  string 
which  holds  it  and  the  cork  will  be  driven  out  by 
the  elastic  force  of  the  carbonic  acid  gas.  The  gas 
performs  its  works,  and  in  so  doing  it  consumes  heat 
and  the  deflection  of  the  thermopile  shows  that  the 
bottle  is  cooler  than  before,  heat  having  been  lost  in 
the  process. 

4.  Any  one  who  examines  the  records  will  soon  find  out  for 
himself  that  those  students  who  'scatter'  most  in  their 
choice  of  studies  are  those  who  accomplish  least  in  any 
of  them;  and  when  he  sees  this  he  ought  to  realize  the 
harm  that  can  be  done  by  a  system  of  absolutely  free 
electives.2 

5.  It  was  a  general  belief  at  St.  Kilda  that  the  arrival  of  a 
ship  gave  all  the  inhabitants  colds.  Dr.  John  Campbell 
took  pains  to  ascertain  the  fact  and  to  explain  it  as  the 
effect  of  eflBuvia  arising  from  human  bodies;  it  was  dis- 

>  Creigbton.  '  Aikins. 


QUESTIONS  AND   EXERCISES  333 

covered,  however,  that  the  situation  of  St.  Kilda  renders 
a  northeast  wind  indispensably  necessary  before  a  ship 
can  make  a  landing.  ^ 

The  great  famine  in  Ireland  began  in  1845  and  increased 
until  it  reached  a  climax  in  1848.  During  this  time  agra- 
rian crime  increased  very  rapidly  until,  in  1848,  it  was 
more  than  three  times  as  great  as  in  1845.  After  this  it 
decreased  with  the  return  of  better  crops  until,  in  1851, 
it  was  only  fifty  per  cent  more  than  in  1845.  It  is  evi- 
dent from  this  that  a  close  relation  of  cause  and  effect 
exists  between  famine  and  agrarian  crime. 
Wages  in  the  United  States  are  higher  than  in  England, 
because  the  former  country  is  a  republic  and  has  a  pro- 
tective tariff. 

In  Sir  Humphry  Davy's  experiments  upon  the  de- 
composition of  water  by  galvanism,  it  was  found  that, 
besides  the  two  components  of  water,  oxygen  and  hydro- 
gen, an  acid  and  an  alkali  were  developed  at  the  two 
opposite  poles  of  the  machine.  The  insight  of  Davy 
conjectured  that  there  might  be  some  hidden  cause  of 
this  portion  of  the  effect:  the  glass  containing  the  water 
might  suffer  partial  decomposition,  or  some  foreign 
matter  might  be  mingled  with  the  water,  and  the  acid  and 
alkali  be  disengaged  from  it,  so  that  the  water  would 
have  no  share  in  their  production.  .  .  .  By  the  substitu- 
tion of  gold  vessels  for  glass,  without  any  change  in  the 
effect,  he  at  once  determined  that  the  glass  was  not  the 
cause.  Employing  distilled  water,  he  found  a  marked 
diminution  of  the  quantity  of  acid  and  alkali  evolved; 
yet  there  was  enough  to  show  that  the  cause,  whatever 
it  was,  was  still  in  operation.  .  .  .  He  now  conceived 
that  the  perspiration  from  the  hands  touching  the  in- 
struments might  affect  the  case,  as  it  would  contain  com- 
mon salt,  and  an  acid  and  an  alkali  would  result  from  its 
decomposition  under  the  agency  of  electricity.  By  care- 
fully avoiding  such  contact,  he  reduced  the  quantity  of 
the  products  still  further  until  no  more  than  slight  traces 
of  them  were  perceptible.  What  remained  of  the  effect 
might  be  traceable  to  impurities  of  the  atmosphere,  de- 

>  Hibben. 


3S4  QUESTIONS  AND   EXERCISES 

composed  by  contact  with  the  electrical  apparatus.  An 
experiment  determined  this :  the  machine  was  put  under 
an  exhausted  receiver,  and,  when  thus  secured  from 
atmospheric  influence,  it  no  longer  evolved  the  acid  and 
the  alkali.^ 
9.  In  a  simple  fracture  of  the  ribs  if  the  lung  be  punctured 
by  a  fragment,  the  blood  eflfused  into  the  pleural  cavity, 
although  freely  mixed  with  air,  undergoes  no  decompo- 
sition. That  is  not  the  case  if  air  enter  directly  through 
a  wound  in  the  chest.  This  difference  in  result  must  be 
causally  connected  with  special  circumstances  —  viz., 
passage  of  air  through  tissues  in  the  lungs.* 

10.  "The  two  females  were  then  seated  upon  two  chairs 
placed  near  together,  their  heels  resting  on  cushions,  their 
lower  limbs  extended,  with  the  toes  elevated  and  the 
feet  separated  from  each  other.  The  object  in  this  ex- 
periment was  to  secure  a  position  in  which  the  ligaments 
of  the  knee-joints  should  be  made  tense  and  no  oppor- 
tunity offered  to  make  pressure  with  the  foot.  We  were 
pretty  well  satisfied  that  the  displacement  of  the  bones 
requisite  for  the  sounds  could  not  be  effected  unless  a 
fulcrum  were  obtained  by  resting  one  foot  upon  the 
other  or  on  some  resisting  body.  The  company,  seated 
in  a  semicircle,  quietly  waited  for  the  'manifestations' 
for  more  than  half  an  hour.  .  .  .  On  resuming  the  usual 
position  on  the  sofa,  the  feet  resting  on  the  floor,  knock- 
ings  very  soon  began  to  be  heard.  .  .  .  The  conclusion 
seemed  clear  that  the  Rochester  knockings  emanate 
from  the  knee  joint."  ' 

11.  Give  two  examples  for  each  of  the  methods,  preferably 
from  ordinary  experience  rather  than  from  science. 

12.  Show  that  Mill's  Methods  imply  a  large  fund  of  relevant 
knowledge. 

13.  Analyze  the  causal  relation  in  such  a  way  as  to  bring 
out  methods  of  testing  supposed  uniformities. 

14.  In  what  way  is  the  Method  of  Difference  an  advance 
upon  the  Method  of  Agreement? 

>  Gore,  The  Art  of  Scientific  Discovery.  *  Russell. 

'  Description  of  the  exposure  of  a  spiritualistic  s^nce,  quoted  by  Podmore,  and 
adapted  by  Taylor. 


QUESTIONS  AND  EXERCISES  335 

15.  By  what  methods  should  the  following  problems  be 
investigated? 

(1)  An  individual  becoming  sick  after  a  meal. 

(2)  The  possibility  of  a  connection  between  rag-weed 
and  hay  fever. 

(3)  The  effect  of  a  new  tariff  upon  the  prosperity  of  a 
country. 

(4)  Education  and  the  decrease  of  superstition. 

(5)  The  relation  between  mosquitos  and  malaria. 

(6)  Bad  eyes  and  criminality. 

(7)  A  crime  and  the  arrest  of  a  suspected  person. 

(8)  The  rapidity  of  growth  of  trees  and  the  kind  of 
soil. 

(9)  Poverty  and  tuberculosis. 

(10)  The  effect  of  radium  upon  cancer. 

CHAPTER  XX 

1.  When  are  statistics  resorted  to?  How  do  they  enable  us 
to  grasp  a  field  which  would  otherwise  be  unmanage- 
able? 

2.  Why  is  definition  of  the  problem  and  of  the  terms  used 
so  important? 

3.  Name  the  stages  of  any  thorough  statistical  investiga- 
tion. What  are  the  special  dangers  confronting  each  of 
these  stages? 

4.  State  the  law  of  statistical  regularity,  and  try  to  explain 
its  foundation. 

5.  In  what  sciences  are  statistics  of  greatest  significance? 
Why? 

6.  Look  up  cases  of  erroneously  interpreted  statistics  and 
show  wherein  the  error  lies. 

7.  "In  Sweden  the  population  and  the  smallpox  mortality 
have  both  been  known  year  by  year  since  1774.  Before 
vaccination  the  mortality  from  smallpox  for  thirty  years 
averaged  2045  per  million.  With  permissive  vaccination 
from  1802  to  1816  it  was  reduced  to  480;  during  seventy- 
seven  years  of  compulsory  vaccination  the  mortality 
averaged  155  per  million;  and  for  ten  years  ending  1894 
it  has  been  down  to  2  per  million.  .  .  . 


86  QUESTIONS  AND  EXERCISES 

*'If  we  compare  the  rate  of  smallpox  mortality  in  the 
different  countries,  we  see  an  enormous  difference  be- 
tween the  well  vaccinated  and  the  badly  vaccinated 
populations.  Here  is  a  table,  given  by  Dr,  Edwardes,  of 
the  mortality  rates  per  miUion  in  the  five  years  1889  to 
1893:  — 

SmalljHXC 

mortality 

per  million 

Germany 2.3 

England  and  Wales 13 . 6 

Chief  French  towns 147. 6 

Italy 180.8 

Belgium 253 

Austria 313 

Spain 638 

Russia,  three  years  only,  including  Asi- 
atic Russia 836 

"In  Germany,  vaccination  and  re  vaccination  are  both 
compulsory.  In  the  other  countries  revaccination  was, 
at  that  time  at  least,  nowhere  enforced."  ^ 

8.  "More  men  than  women  die  every  year.  This  is  due  to 
the  greater  mortality  attending  the  life  of  the  male."  * 
What  does  this  mean?  How  can  it  be  possible?  "In 
Germany  109  men  die  each  year  for  every  100  women." 
What  can  we  conclude  from  this?  Why  is  it  better  to 
know  that  in  Germany  28.6  out  of  every  thousand  males 
die  each  year  and  25.3  out  of  every  thousand  females? 
Since  everybody  must  die  sooner  or  later  how  is  it  possible 
that  there  should  be  in  any  country  (or  in  the  whole 
world)  a  permanently  greater  death-rate  for  one  sex 
than  for  the  other? 

9.  Show  the  importance  of  the  qualitative  side  of  social 
phenomena.  Why  are  quantitative  data  apt  to  be  mis- 
leading in  certain  fields? 

>  Edinburgh  Review,  vol.  189,  pp.  350-62. 
*  Mayo-Smith,  Statisiun  and  Sociology. 


QUESTIONS  AND  EXERCISES 


887 


10.  Interpret  the  following  statistics:  — 

A  table  giving  the  percentage  of  accidents  occurring 
according  to  the  time  of  the  day 


Time 

19.-  S  A.M. 

8-  6  A.M, 

6-9  A.M. 

9-12  A.M. 

12-3  P.M. 
3-  6  p.m. 
6-9  P.M. 
9-12  P.M. 


Germany 

1.93 

2.55 
13.87 
28.42 
13.81 
26.62 

9.25 

3.85 


Italy 

1.09 

2.47 

15.40 

29.20 

14.55 

26.48 

7.83 

2.54 


11.  Study  carefully  some  one  chapter  of  Mayo-Smith's  StatiS' 
tics  and  Sociology  with  especial  attention  to  the  reflective 
analysis  which  he  gives  at  the  end  of  the  chapter. 

12.  What  statistical  investigations  would  seem  to  you  very 
important  for  a  modern,  democratic  society? 
In  the  United  States  census  of  1890,  the  question  of 
color  —  whether  black,  mulatto,  quadroon,  or  octoroon 
—  was  asked.  Why  was  such  a  question  faulty  from  the 
standpoint  of  statistics? 

Point  out  the  sociological  bearing  of  the  following  statis- 
tics from  the  United  States  Life  Tables:  Of  100,000 
negro  females,  18,507  die  before  the  age  of  one  year, 
while  of  100,000  white  females,  10, 460  die  before  reaching 
the  same  age. 

15.  It  is  undeniable  that  tenancy  is  increasing  in  the  United 
States.  From  the  Twelfth  Census,  we  have  the  follow- 
ing comparison:  — 


13 


14 


Total 
number 
of  farms 

Number  operated  by 

Ovmers 

Cash 
tenants 

Share 
tenants 

1880 

4,008,907 
5.739,657 

2,984,306 
3,713,371 

322,357 
752,920 

702,244 

1900 

1,273,366 

338  QUESTIONS  AND   EXERCISES 

The  Marxian  Socialist  maintains  that  this  increase 
proves  concentration  in  farming.  Does  any  other  ex- 
planation suggest  itself  to  you? 

CHAPTER  XXI 

1.  Under  what  conditions  can  science  predict  with  accu- 
racy the  occurrence  of  particular  events?  Give  concrete 
examples. 

2.  Are  eflfects  always  found  when  their  causes  are  present?  Be 
prepared  to  defend  your  answer  by  means  of  instances. 

3.  What  does  each  of  the  following  propositions  mean? 

(1)  The  child  will  probably  catch  the  measles. 

(2)  The  earth  will  probably  grow  colder  in  the  distant 
future. 

(3)  The  probability  in  favor  of  a  long  life  for  a  man 
of  his  profession  is  very  great. 

4.  Distinguish  between '  probability '  and '  objective  chance.' 
How  can  you  harmonize  the  existence  of  probability 
with  the  Principle  of  the  Uniformity  of  Nature? 

5.  Is  there  any  diflPerence  between  saying  that  a  certain 
horse  is  the  most  likely  to  win  the  race  and  saying  that 
it  is  likely  to  win?  ^ 

6.  How  should  life-insurance  statistics  be  interpreted?  Can 
they  be  made  to  apply  to  any  one  individual?  If  so,  in 
what  sense? 

7.  What  reply  can  be  made  to  the  following?  "You  say 
that  the  prisoner  is  probably  guilty.  I  grant  it.  But  this 
only  means  that  the  prisoners  in  most  cases  of  this  sort 
are  guilty.  It  does  not  mean  that  this  particular  prisoner 
has  even  a  touch  of  guilt.  Your  very  use  of  the  word 
'probable'  is  a  confession  that  for  all  you  know  he  may 
be  absolutely  innocent.  How  then  can  you  ask  the  jury 
to  condemn  him  to  an  awful  fate?"  ^ 

8.  Discuss  the  following  statement:  "Nine  times  out  of 
ten  we  can  act  only  on  probability." 

9.  What  is  the  probability  that  a  die  will  fall  with  the  same 
side  up  four  times  in  succession? 

10.  What  is  the  probability  that  you  will  draw  either  an 
ace  or  a  five  of  hearts  from  a  full  deck  of  cards? 

1  Aikina.  '  Aikins. 


QUESTIONS   AND  EXERCISES  S39 

11.  "The  regularities  of  the  mass  have  no  compelling  force 
over  the  individual,"  ^  Against  what  fallacy  is  this  state- 
ment directed? 


CHAPTER  XXII 

1.  Give  some  common  examples  of  the  use  of  an  arithmetical 
average.  Explain  such  an  expression  as  the  *  average 
rate  of  interest.' 

2.  Show  that  percentage  of  increase  in  the  population  of  a 
town  or  city  is  a  case  of  arithmetical  average. 

3.  What  average  would  be  of  most  use  for  the  following? 

(1)  The  standard  size  of  a  manufactured  article. 

(2)  A  stock  of  hats  for  a  clothing  store. 

(3)  The  physical  estimation  of  a  varsity  crew. 

(4)  The  salary  of  teachers. 

4.  Find,  or  work  out,  a  set  of  statistics  and  discover  the 
mode  and  the  median. 

5.  Examine  critically  the  phrase,  *  the  average  man.*  What 
danger  of  misinterpretation  lurks  behind  the  phrase? 

6.  Why  are  graphical  methods  being  used  so  freely  at  the 
present  time? 

7.  Find  at  least  five  devices  for  graphical  representation  in 
common  use  and  compare  their  effectiveness.^ 

8.  Look  up  cases  of  graphical  representation  in  the  popular 
magazines  and  make  a  report  upon  at  least  four  which 
particularly  attracted  your  attention. 

9.  "An  average  must  not  be  a  mere  numerical  average,  for 
that  amounts  to  nothing.  It  must  be  a  typical  average, 
expressive  of  about  what  the  real  condition  of  things  is." 
Explain  this  statement  in  the  light  of  the  preceding 
chapters. 

CHAPTER  XXIII 

1.  Contrast  'scientific  investigation*  and  'judicial  proof* 
as  regards  their  methods  and  social  surroundings. 

2.  Estimate  the  following  arguments:  — 

(1)  If  you  believe  in  the  survival  of  the  fittest,  you 
must  believe  that  this  old  manuscript  was  one  of 

•  Mayo-Smith.  *  See  Brinton  on  this  question. 


340  QUESTIONS  AND  EXERCISES 

the  best  of  its  time,  for  it  is  the  only  one  that 
has  survived. 

(2)  This  book  is  authentic;  then  why  should  we  not 
believe  what  it  says? 

(3)  This  text  of  Cicero  dates  from  the  twelfth  century 
and  that  dates  only  from  the  fourteenth;  then 
why  is  n't  this  a  better  one  to  go  by  than  that? 

(4)  This  text  has  great  value  for  the  historian,  for  it 
was  restored  at  infinite  pains,  and  there  is  now 
every  reason  to  believe  that  it  is  substantially 
correct. 

(5)  "Come  and  have  your  fortune  told  by  Blank's 
system  of  palmistry.  No  man  of  science  has  ever 
disputed  the  claims  of  this  system."  ^ 

3.  Take  any  striking  criminal  case  before  the  courts  and 
work  out  the  circumstantial  evidence  for  and  against  the 
issue  in  the  way  suggested  in  the  text. 

4.  What  is,  in  your  opinion,  the  comparative  probative 
value  of  circumstantial  and  testimonial  evidence? 

5.  Connect  the  possibility  of  a  plurality  of  causes  with  the 
methods  used  in  explaining  events. 

6.  What  seems  to  you  to  be  a  reasonable  doubt? 

7.  Examine  the  following  case.  Do  you  think  that  there 
was  a  reasonable  doubt  of  Bradford's  guilt? 

"Jonathan  Bradford,  in  1736,  kept  an  inn,  in  Ox- 
fordshire, on  the  London  road  to  Oxford.  He  bore  a 
very  exceptional  character.  Mr.  Hayes,  a  gentleman 
of  fortune,  being  on  his  way  to  Oxford,  on  a  visit  to 
a  relation,  put  up  at  Bradford's.  He  there  joined  com- 
pany with  two  gentlemen,  with  whom  he  supped,  and, 
in  conversation,  unguardedly  mentioned  that  he  had 
then  about  him  a  sum  of  money.  In  due  time  they 
retired  to  their  respective  chambers;  the  gentlemen 
to  a  two-bedded  room,  leaving,  as  is  customary  with 
many,  a  candle  burning  in  the  chimney  corner.  Some 
hours  after  they  were  in  bed,  one  of  the  gentlemen, 
being  awake,  thought  he  heard  a  groan  in  an  adjoining 
chamber;  and  this  being  repeated,  he  softly  awaked 
his  friend.  They  listened  together,  and  the  groans 
increasing,  as  of  one  dying  and  in  pain,  they  both 

>  Aikins. 


QUESTIONS  AND  EXERCISES  341 

instantly  arose  and  proceeded  silently  to  the  door  of 
the  next  chamber,  whence  they  had  heard  the  groans, 
and,  the  door  being  ajar,  saw  a  light  in  the  room.  They 
entered,  and  perceived  a  person  weltering  in  his  blood 
in  the  bed,  and  a  man  standing  over  him  with  a  dark 
lantern  in  one  hand  and  a  knife  in  the  other!  The  man 
seemed  as  petrified  as  themselves,  but  his  terror  car- 
ried with  it  all  the  terror  of  guilt.  The  gentlemen  soon 
discovered  that  the  murdered  person  was  the  stranger 
with  whom  they  had  that  night  supped,  and  that  the 
man  standing  over  him  was  their  host.  They  seized 
Bradford  directly,  disarmed  him  of  his  knife,  and 
charged  him  with  being  the  murderer.  He  assumed, 
by  this  time,  the  air  of  innocence,  positively  denied 
the  crime,  and  asserted  that  he  came  there  with  the 
same  humane  intentions  as  themselves;  for  that,  hear- 
ing a  noise,  which  was  succeeded  by  a  groaning,  he 
got  out  of  bed,  struck  a  light,  armed  himself  with  a 
knife  for  his  defense,  and  was  but  that  minute  entered 
the  room  before  them.  These  assertions  were  of  little 
avail;  he  was  kept  in  close  custody  till  the  morning, 
and  then  taken  before  a  neighboring  justice  of  the 
peace.  Bradford  still  denied  the  murder,  but,  never- 
theless, with  such  apparent  indications  of  guilt,  that 
the  justice  hesitated  not  to  make  use  of  this  most  ex- 
traordinary expression,  on  writing  out  his  mittimus, 
*Mr.  Bradford,  either  you  or  myself  committed  this 
murder.' " 

8.  How  does  the  mind  work  in  passing  judgment  upon  a 

very  complex  case?  Study  your  own  method  of  reach- 
ing a  conclusion  in  some  particular  problem  of  a  high 
degree  of  complexity. 

9.  Analyze  one  of  Conan  Doyle's  Sherlock  Holmes  stories 

to  see  just  how  the  circumstantial  evidence  is  used 
both  to  lead  and  to  mislead. 
10.  What  is  the  fallacy  of  'neglected  factor'?   Give  at  least 
two  examples  which  have  come  within  your  experi- 
ence.* 

*  If  the  teacher  can  secure  the  book,  he  will  find  many  interesting  examples  for  all 
the  difficulties  confronting  evidence  in  Wigmore's  Prineiplei  of  Jvdicial  Proof.  These 
examples  are  too  long  to  quote  in  the  present  test. 


342  QUESTIONS  AND   EXERCISES 

11.  Look  up  the  investigation  of  some  historical  myth  like 

that  of  William  Tell.  What  is  its  interest  to  the  lo- 
gician? 

12.  Newton  was  of  the  opinion  that  oral  tradition  could  be 

trusted  for  eighty  years  after  the  event.  Others  have 
named  forty  years.  Why  are  such  estimations  rather 
absurd? 

13.  It  is  asserted  by  many  recent  historians  of  the  American 

Revolution  that  our  school  histories  contain  a  deal 
of  myth  along  with  a  fair  percentage  of  fact.  What 
causes  might  lead  to  legend  and  myth  about  the 
founders  of  the  American  Republic? 

CHAPTER  XXIV 

1.  What  is  the  nature  of  explanation? 

2.  Take  any  two  problems  which  have  arisen  lately  in  your 
experience  and  try  to  grasp  the  exact  character  of  the 
explanation  given  them. 

3.  What  is  meant  by  the  'sentiment  of  rationality'?  Show 
that  it  depends  upon  the  constitution  of  our  minds. 

4.  Is  explanation  possible  apart  from  concepts? 

5.  Apply  Dewey's  analysis  of  the  role  of  concepts  to  at 
least  two  cases  of  interpretation,  stressing  identification, 
supplementation,  and  placing  in  a  system. 

6.  What  difference  of  setting  have  the  two  terms,  'proof 
and  'explanation'?  What  have  they  in  common? 

7.  How  are  induction  and  deduction  united  in  the  process 
of  explanation?  Illustrate  by  examples  either  from  prac- 
tical life  or  from  science. 

8.  Are  all  systems  equally  tentative?  Can  you  think  of  any 
system  which  seems  to  you  to  be  in  final  shape? 

9.  How  would  you  distinguish  between  'general'  and  'spe- 
cific' explanation? 

10.  What  principle  would  you  adopt  as  a  means  of  arranging 
the  sciences  in  an  orderly  fashion?  Do  you  think  that 
such  an  ordering  of  them  gives  a  penetrative  classifica- 
tion? 

11.  Why  is  mathematics  usually  spoken  of  as  'deductive'? 
Does  this  seem  to  you  the  best  term  that  could  be 
used? 


QUESTIONS   AND  EXERCISES  343 

12.  Examine  historical  investigation  in  the  light  of  your 
present  knowledge  of  logic.  Show  especially  that  all  facts 
are  judgments. 

CHAPTER  XXV 

1.  Distinguish  clearly  between  'consistent  thinking*  and 
*  true  thinking.* 

2.  What  is  meant  by  'logical  necessity'? 

3.  State  and  explain  the  'Laws  of  Thought.' 

4.  What  principles  are  implied  in  all  investigation  which 
seeks  to  determine  truth.-* 

5.  How  would  you  formulate  your  conception  of  the  inter- 
nal criteria  of  truth? 

6.  Explain  the  conception  of  degrees  of  belief.  Relate  your 
views  to  the  modality  of  judgments. 

7.  Does  language  express  adequately  the  different  degrees 
of  belief  we  actually  hold? 

8.  Show  that  the  meaning  of  knowledge  is  intimately  bound 
up  with  the  meaning  of  truth. 

9.  Read  Tennyson's  In  Memoriam,  xxxiv.  Does  it  seem 
to  you  to  imply  an  appeal  to  a  standard  of  truth  other 
than  the  logical? 

10.  Be  prepared  to  defend  James's  position  or  Clifford's  ac- 
cording as  the  one  or  the  other  strikes  you  as  the  sounder. 


INDEX 


(KiNDLT  AHBANQED  BY  Mb.  DoUGLAS  ClAJPPERTON) 


Absolute  term.  29,  34. 

Abstract  sciences,  288. 

Accident,  fallacy  of,  148. 

Agreement  and  difference,  joint 
method  of,  215,  217. 

Agreement,  method  of,  215,  217. 

Aikins,  quoted,  249,  270. 

Ambiguity,  41;  causes  of,  41. 

Ambiguous  terms,  fallacy  of,  143. 

Amphiboly,  144. 

Analogy,  as  basis  of  reasoning, 
208;  false,  209. 

Analytic  division,  59. 

Apodeictic  judgment,  301. 

Argumentum  ad  Hominem,  153; 
ad  igTiorantiam,  154;  ad  popu- 
lum,  153;  ad  cerecundiam,  155. 

Aristotle's  definition  of  syllog- 
ism, 107. 

Arithmetical  average,  252,  257. 

Assertions,  76,  79. 

Assertoric  judgment,  301. 

Average,  geometric,  256,  257; 
median,  256,  257;  uses  of,  251; 
weighted,  253,  257. 

Bain,  quoted,  236. 

Belief,  degrees  of,  301. 

Bode,  quoted,  15,  30,  35,  157, 

210,  221,  243,  277. 
Bosanquet,  quoted,  85,  197. 
Bowley,  quoted,  229,  253. 
Brinton,  quoted,  258,  262. 
Burrill,  quoted,  265. 

Carhart,  quoted,  222. 
Cartograms,  257. 


Categorematic  words,  28. 

Cause,  definition  of,  211. 

Certainty,  possibility  of,  in  fore- 
casting events,  240. 

Change  in  meaning  of  words, 
44. 

Circumstantial  evidence,  265; 
nature  of,  267;  circumstantial 
and  testimonial  evidence,  266. 

Classes,  51;  coordination  of,  55; 
subordination  of,  55;  super- 
ordination  of,  55. 

Classification,  artificial,  52,  53; 
definition  of,  50;  diagnostic, 
53;  index,  53;  natural,  52,  53. 

Classificatory  division,  60. 

Clifford,  quoted,  309,  310. 

Collective  terms,  33. 

Complex  question,  151. 

Composition,  fallacy  of,  144. 

Concepts,  20,  96;  use  of,  in 
explanation,  280. 

Concomitant  variations,  method 
of,  221. 

Concrete  logic,  5. 

Concrete  sciences,  290,  291. 

Concrete  term,  30. 

Conditions  and  occasions  of 
thought,  15;  personal  condi- 
tions, 17. 

Connotation,  37,  38. 

Consistent  thinking,  nature  of, 
294;  relation  to  truth,  294. 

Constancy  of  averages,  233,  245. 

Constituent  species,  57. 

Contradiction,  law  of,  207. 

Contradictories,  100. 


346 


INDEX 


Contraries,  100. 

Conversion,  102;  by  contraposi- 
tion, 105;  by  limitation,  102; 
simple,  102. 

Coordinate  species,  57. 

Copula,  28. 

Correlatives,  S4. 

Creighton,  quoted,  34,  137. 

Darwin,  quoted,  192;  from 
Creighton,  204. 

Davidson,  quoted.  44,  62,  69. 

Definition,  nature  of,  64;  pur- 
pose of,  63,  64;  definition  and 
classification,  66. 

Definition  of  logic,  1. 

Denotation,  37,  38. 

Dewey,  quoted,  11,  169,  176, 
178,  203,  279,  282. 

Dichotomous  division,  58,  59. 

Dictum,  301. 

Difference,  method  of,  219. 

Differentia,  57. 

Dilemma,  137. 

Direct  evidence,  269. 

Discovery  and  proof,  11. 

Disjunctive  syllogism,  136. 

Distribution  of  terms,- 94. 

Division,  56. 

Division,  fallacy  of,  145. 

Doubt,  logic  of,  309. 

Empirical  logic,  5. 
Enthymeme,  126. 
Episyllogisms,  127. 
Equivocal  words,  43. 
Erroneous  perception,  cause  of, 

189. 
Events,  prediction  of,  239. 
Evidence,  convergence  of,  268; 

fallacies  in  weighing  evidence, 

275. 
Exceptive  proposition,  93. 
Excluded  middle,  law  of;  297. 
Exclusive  propositions;  93. 


Experimentation,  177;  in  biol- 
ogy, 179;  in  psychology,  180. 

Explanation,  general,  287;  levels 
of,  285;  nature  of,  278;  and 
proof,  282;  specific,  287. 

Extension,  37. 

Extra-syllogistic  reasoning;  129. 

Fact,  theory  and,  24,  25. 
Facts,  194;  relevant,  195. 
Fallacies,  141;  classification  of, 

142;  deductive,  142. 
Fallacy,    of    four    terms,    112; 

of  unwarranted  assumption, 

149. 
Figure   of    speech,   fallacy   of, 

148. 
Figures  of  the  syllogism,  118. 
Frequency  graphs,  262. 
Fundamentum  divisionis,  67. 

General  term,  32. 

Genus,  56. 

Geometric  average,  256,  257. 

Gibson,  quoted,  144,  146,  149, 
152. 

Giffen,  quoted,  230. 

Graphs,  cartogram,  257;  fre- 
quency, 262;  and  graphical 
methods,  257;  pictogram,  268. 

Gross,  quoted,  271. 

Helmholtz,  quoted,  286. 

Hibben,  quoted,  54,  237. 

Historical  science,  290,  291. 

History  of  logic,  160. 

Huxley,  quoted,  199. 

Hypotheses,  definition  of,  197; 
development  of,  205 ;  function 
of,  182;  kinds  of,  198;  origin 
of,  200;  proof  of,  206;  value 
of,  203;  hypothesis,  theory 
and  fact,  207. 

Hypothetical  syllogism,  132; 
rule  of,  134. 


INDEX 


847 


Identity,  law  of,  296. 
Immediate  inference,  98. 
Indefinite  propositions,  90. 
Induction  and  deduction,  159. 
Inductive  logic,  5. 
Inertia  of  large  numbers,  law  of, 

233. 
Inferential  element  in  precepts, 

21. 
Infimse  species,  57. 
Intention,  37. 
Introductory  logic,  5. 
Intuitive  mind,  202. 
Irrational  evidence,  fallacy  of, 

152. 
Irrelevant  conclusion,  156. 

James,    quoted,    23,    180,    204, 

297,  304,  305,  306,  307. 
Jevons,   quoted,   54,   148,   177, 

189,  226,  242. 
Jones,  quoted,  66, 104, 128,  223, 

249,  272. 
Joseph,  quoted,  3,  4,  60,  130, 

146,  286,  289. 
Judgment,  27;  and  concepts,  81; 

definition  of,  84;  levels  of,  80; 

relation  of,  to  knowledge,  84. 
Judicial  proof,  264;  difficulties 

confronting,  265. 

Kinds  of  logic,  4. 
King,   quoted,   228,   229,   230, 
234,  248.  252,  256. 

Langlois  and  Seignobos,  quoted, 
290,  292. 

Language,  48;  law  of,  in  logic,  6; 
purpose  of,  87. 

Law  of  contradiction,  297;  of 
excluded  middle,  297;  of  iden- 
tity, 296;  of  language,  6. 

Laws  of  thought,  296. 

Legal  reasoning,  264. 

Locke,  quoted,  63, 108, 152, 155. 


Lodge,  quoted,  16. 

Logic,  definition  of,  1;  as  ap- 
plied science,  3;  kinds  of,  4; 
value  of,  2;  concrete,  6;  em- 
pirical, or  inductive,  5;  intro- 
ductory, 5;  material  of,  7; 
relation  of,  to  other  sciences, 
6;  symbolic,  5;  of  systematic 
investigation,  159. 

Lotze,  quoted,  147. 

McDougall,  quoted,  179. 

Macleane,  quoted,  48,  71,  73. 

Major  term,  11. 

Material  of  logic,  7. 

Mayo-Smith,  quoted,  232. 

Meaning  of  terms,  38. 

Measurement,  importance  of, 
177. 

Median,  256,  257. 

Mellone,  quoted,  219. 

Memory,  errors  of,  192. 

Middle  term,  110. 

Mill,  quoted,  208,  226. 

Mill's  methods  of  testing  con- 
nections, 214;  method  of 
agreement,  215;  of  difference, 
219. 

Minor  term.  111. 

Minto,  quoted,  47,  48,  92,  107, 
124,  162,  217,  233. 

Mode,  255,  257. 

Modus  ponens,  133;  tollens,  133. 

Moods,  of  syllogisms,  118. 

Multiple  working  hypotheses, 
method  of,  205. 

MUnsterberg,  quoted,  186,  188. 

Negative  correlation,  236. 
Negative  term,  56. 
Non-sequitur,  157. 

Observation,  conditions  of,  185. 

Ob  version,  103. 

Opposition  of  propositions,  99. 


348 


INDEX 


Partitive  propositions,  93. 

Percept,  definition  of,  20,  21; 
inferential  element  in,  21. 

Perception,  errors  in,  187. 

Petitio  principii,  149. 

Pictograms,  258. 

Pillsbury,  quoted,  13, 19, 62, 288. 

Positive  term,  36. 

Post  hoc,  ergo  propter  hoc,  212. 

Postulates  of  logic,  298. 

Predicables,  73. 

Preindesignate  propositions,  90. 

Privitive  term,  37. 

Probabilities,  mistakes  in  inter- 
pretation of,  248. 

Probability,  meaning  of,  240; 
empirical,  242;  based  on  aver- 
ages, 243;  and  chance,  241; 
contrasted  with  certainty, 
241;  estimating  kinds  of,  242; 
probability  in  regard  to 
events,  241;  in  regard  to 
principles,  241. 

Problem  of  generalization,  167. 

Problematic  judgment,  301. 

Processes  preliminary  to  reflec- 
tive thought,  20. 

Proof,  and  explanation,  282;  and 
discovery,  11. 

Propositions,  27,  76,  98,  cate- 
gorical, 89;  disjunctive,  89; 
hypothetical,  89;  quality  of, 
89;  quantity  of,  89. 

Prosyllogisms,  127. 

Proximum  genus,  57. 

Psychologist's  view  of  reason- 
ing, 13. 

Quality  of  propositions,  89,  90. 
Quantity  of  propositions,  89,  90. 
Quetelet,  quoted,  245. 

Real  definition,  64. 
Reasoning,    examples    of,    14; 
psychologist's  view  of,  13. 


Reflective  mind,  202. 

Reflective  thought,  processes 
preliminary  to,  20. 

Relation  of  logic  to  other  sci- 
ences, 6. 

Relative  term,  34. 

Residues,  method  of,  224. 

Ribot,  quoted,  201,  202. 

Romanes,  quoted,  23. 

Rules,  of  definition,  69-71;  of 
division,  58;  for  mathematical 
probability,  246;  of  syllogism, 
112. 

Russell,  quoted,  284 

Schiller,  quoted,  117. 

Science,  development  of,  173; 
method  of  graphs  in,  181; 
statistical  method  in,  180. 

Scientific  investigation,  264. 

Sellars,  quoted,  305. 

Setting  of  thought,  17. 

Sidgwick,  quoted,  3,  25,  51,  68, 
209,  214. 

Sigwart,  quoted,  278. 

Singular  term,  30,  31. 

Smith,  quoted,  44. 

Sociology  of  logic,  16. 

Socratic  dialectic,  67. 

Sorites,  128;  Aristotelian,  128; 
Goclenian,  129. 

Species,  56. 

Square  of  opposition,  100. 

Statistical  investigation,  stages 
in,  230. 

Statistical  regularity,  law  of, 
232. 

Statistics,  definition  of,  229;  in 
causal  relations,  236;  dangers 
in  use  of,  233;  inertia  of  large 
numbers,  233;  value  of,  235. 

Steps  in  systematic  investiga- 
tion, 166. 

Stout,  quoted,  40. 

Subalterns,  100. 


INDEX 


349 


Subcontraries,  100. 

Summum  genus,  57. 

Syllogism,  axiom  of,  110;  de- 
fined, 107;  disjunctive,  136; 
elements  of,  110;  figures  of, 
118;  function  of,  162;  hypo- 
thetical, 132;  moods  of,  118; 
nature  of,  107;  rules  of,  112. 

Symbolic  classification  of  propo- 
sitions, 91. 

Symbolic  logic,  5. 

Syncategorematic  words,  28. 

Synthetic  classification,  59. 

Systems  of  knowledge,  typical, 
288. 

Systems,  tentative  nature  of,  283. 

Taylor,  quoted,  56,  154. 
Technique     and     instruments, 

value  of,  175. 
Terms,  27,  28. 

Testimonial  evidence,  266,  269. 
Testimony,   definition  of,   270; 

critical  attitude  toward,  270; 

errors  in,  193;  logical  tests  of, 

273. 
Theory  and  fact,  24,  25. 
Thinking,     definition    of,     18; 

purpose  of,  18. 


Thought,  conditions  and  occa- 
sions of,  15;  laws  of,  296; 
setting  of,  17;  what  is,  10. 

True  idea,  definition  of,  303. 

Truth,  298;  criteria  of,  299; 
definitions  of,  304;  meaning 
of,  303;  pragmatic  definition 
of,  304;  truth  and  validity, 
299;  and  will  to  believe,  805. 

Tyndall,  quoted,  200. 

Uniformity  of  nature,  principle 

of,  170. 
Univocal  words,  43. 

Vagueness,     46;     of     abstract 

terms,  47. 
Value  of  logic,  2. 
Verbal  definition,  64. 
Verification,  300. 
Vincent,  quoted,  291. 

Weighted  average,  253,  257. 
Wei  ton,  quoted,  198,  246,  247. 
Whately,  quoted,  156. 
Whewell,  quoted,  8. 
Whitehead,  quoted,  289. 
Wigmore,   quoted,   270,  271, 
274. 


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